White Noise

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This correspondence describes a method for estimating the parameters of an autoregressive (AR) process from a finite number of noisy measurements. The method uses a modified set of Yule-Walker (YW) equations that lead to a quadratic eigenvalue problem that, when solved, gives estimates of the AR parameters and the measurement noise variance.

This paper proposes a generation mechanism for cyclostationary and self-similar processes. The proposed model extracts the information from the immediate coarser scale and adds the innovations to it to obtain the finer scale representation of the stochastic process. Basic block of the proposed model is the subband coder. By cascading the blocks of subband coder and passing white noise as one of input in addition to coarser information at each stage, cyclostationary process is generated. For generation of selfsimilar processes, white noise input for each stage is given in particular fashion. The mapping from finer scale to the immediate coarser scale is obtained using proposed blurring model. We have also given scheme for estimation of parameters of the proposed generation mechanism. The parameters are estimated for a given statistics case as well as the given data case. The proposed model can be used in variety of applications such as speech and image processing, biomedical signal processing, seismic data processing etc. Index Terms-Modeling, statistically matched, stochastic processes, self-similar and cyclostationary process, parameter estimation, filter banks.

The optimum parameters of multiple tuned mass dampers (MTMD) for suppressing the dynamic response of a base-excited structure in a specific mode is investigated. The base excitation is modelled as a stationary white noise random process. The stationary response of the structure with MTMD is analyzed for the optimum parameters of the MTMD system. The criterion selected for optimality is the minimization of the root mean square (r.m.s.) displacement of the main structure. The parameters of MTMD that are optimized include the damping ratio, the tuning frequency ratio and the frequency bandwidth of the MTMD system. The optimum parameters of the MTMD system and corresponding effectiveness are obtained for different damping ratios of the main structure and mass ratios of the MTMD system. In addition, the effectiveness of an optimally designed MTMD system is compared with that of an optimum single tuned mass damper. It is shown that the optimally designed MTMD system is more effective for ...

We study the role of multiplicative colored noise for different values of the correlation time τc in the dynamics of two competing species, described by generalized Lotka-Volterra equations. The multiplicative colored noise models the interaction between the species and the environment. The interaction parameter between the species is a random process which obeys a stochastic differential equation with a generalized bistable potential in the presence of a periodic driving term, which accounts for the environment temperature variation. The bistable potential is useful to describe the coexistence and exclusion dynamical regimes of the ecosystem. Noise-induced periodic oscillations of the species concentrations and stochastic resonance phenomenon appear due to the presence of the multiplicative noise. We find that for low values of the correlation time τc the response of the system coincides with that obtained with multiplicative white noise. For higher values of τc the coherent response of the system and the maximum of the signal-to-noise ratio, signature of the stochastic resonance phenomenon, are shifted towards higher values of the noise intensity.

Accurate and detailed noise calculations for operational amplifier circuits using MATLAB are proposed. The analysis of the basic op amp circuits (inverting, non-inverting and differential circuits) is performed taking into account the specifics of current and voltage amplifiers. The MATLAB function m-files are developed to predict the noise. The following characteristics are calculated: total output spot noise voltage; total equivalent

An algorithm for estimating the basis vectors used in the Karhunen-Loeve Transform (KLT) is described. The algorithm is "blind" in the sense that it utilizes minimal information about the data vector being encoded. It is capable of estimating the KLT basis vectors using only the KLT coefficients and one additional scalar quantity. This eliminates the need to repeatedly encode and transmit the KLT basis vectors.

This work is organized as follows. In Section 11, we present some background on tree searching and the SA, and we formulate the basic structure of our simulation algorithms. After first reviewing IS fundamentals for coded communications systems, Section 111 presents two IS schemes for estimating the SA distribution of computation. These are the reference path method and the partitioning method.

This study investigated the relationship between aversive conditioning, heart rate variability suppression, behavioral activation system/behavioral inhibition system and risk-avoidance on the Iowa gambling task (IGT) in a nonclinical sample (29 male, 29 female, mean age = 20.7). A laboratory based Pavlovian aversive conditioning paradigm was used where a 1500 Hz tone (CS?) was followed by a burst of loud white noise (US), and a 850 Hz (CS-) tone was never followed by the US. In a subsequent extinction phase where the CS? and CS-were presented without the US, conditioned skin conductance responses to the CS? indicated aversive conditioning. The results showed that the participants who did not show aversive conditioning (N = 26) exhibited significantly less risk-avoidance compared to participants who did show aversive conditioning (N = 32). Regression analysis showed that among the study variables, only aversive conditioning contributed significantly to explaining variance in risk-avoidance. These results may have implications for understanding risk-taking in gambling in general, and may be a starting point understanding the role of aversive conditioning in the development and maintenance of gambling problems.

Noise can significantly impact the effectiveness of video processing algorithms. This paper proposes a fast white-noise variance estimation that is reliable even in images with large textured areas. This method finds intensity-homogeneous blocks first and then estimates the noise variance in these blocks, taking image structure into account. This paper proposes a new measure to determine homogeneous blocks and a new structure analyzer for rejecting blocks with structure. This analyzer is based on high-pass operators and special masks for corners to stabilize the homogeneity estimation. For typical video quality (PSNR of 20-40 dB), the proposed method outperforms other methods significantly and the worst-case estimation error is 3 dB, which is suitable for real applications such as video broadcasts. The method performs well both in highly noisy and good-quality images. It also works well in images including few uniform blocks.

This article presents a review of reverse correlation in neurophysiology. We discuss the basis of reverse correlation in linear transducers and in spiking neurons. The application of reverse correlation to measure the receptive fields of visual neurons using white noise and m-sequences, and classical findings about spatial and color processing in the cortex resulting from such measurements, are emphasized. Finally, we describe new developments in reverse correlation, including "sub-space" and categorical reverse-correlation. Recent results obtained by applying such methods in the orientation, spatial-frequency and Fourier domains have revealed the importance of cortical inhibition in the establishment of sharp tuning selectivity in single neurons.

This correspondence presents the Barankin bound as a fundamental statistical tool for the understanding of the threshold effect associated with the estimation of the frequency of a sinusoid in additive white Gaussian noise. It is shown that the threshold effect takes hold whenever the Barankin bound departs significantly from the Cramer-Rao bound. In terms of the signal-to-noise ratio (SNR) and the data length T , the quantity SNR 2T=ln T is shown to be a good indicator for deciding whether the SNR is above threshold or not.

A second-order non-linear non-autonomous electronic circuit, which contains an amplifier, two integrators and a comparator, is studied. For a certain set of values for the circuit's parameters (amplitude and frequency of the driving signal and R C values), the circuit's output signal is non-periodic. From the numerically calculated output signal, the correlation dimension and the Kolmogorov entropy are derived. Their values prove that the dynamical system realized by the studied circuit is a deterministic chaotic one. Moreover, the influence of artificial white noise on the original signal was investigated and the results show that only noise levels higher than 1% begin to affect the signal significantly.

Online partial discharge (PD) detection still remains a very challenging task because of the strong electromagnetic interferences. In this paper, a new method of de-noising, using complex Daubechies wavelet (CDW) transform, has been proposed. It is a relatively recent enhancement to the real-valued wavelet transform because of two important properties, which are nearly shift invariant and availability of phase information. Those properties give CDW transform superiority over other real-valued wavelet transform. On the basis of CDW transform, complex threshold algorithm and combined information are devised. In order to take into account the difference of the real part and imaginary part of complex wavelet coefficients, complex threshold is devised to modify the real part and imaginary part respectively. Because the restored signal by inverse CDW transform is complex one, combined information is devised to combine the real part and imaginary part of complex signal to construct a real one, furthermore making full use of the simple information from complex signal.

Presents a globally asymptotically stabilizing (GAS) controller for regulation and dynamic positioning of ships, using only position measurements. It is assumed that these are corrupted with white noise hence a passive observer which reconstructs the rest of the states is applied. The observer produces noise-free estimates of the position, the slowly varying environmental disturbances and the velocity which are used

In this paper a non-linear extension to the synthetic discriminant function (SDF) is proposed. The SDF is a well known 2-D correlation filter for object recognition. The proposed nonlinear version of the SDF is derived from kernel-based learning. The kernel SDF is implemented in a nonlinear high dimensional space by using the kernel trick and it can improve the performance of the linear SDF by incorporating the image's class higher order moments. We show that this kernelized composite correlation filter has an intrinsic connection with the recently proposed correntropy function. We apply this kernel SDF to face recognition and simulations show that the kernel SDF significantly outperforms the traditional SDF as well as is robust in noisy data environments.

EEG time series were modeled as an output of the linear filter driven by white noise. Parameters describing the signal were determined in a way fulfilling the maximum entropy principle. Transfer function and the impulse response function were found. The solutions of the differential equations describing the system have the form of the damped oscillatory modes. The representation of the EEG time series as a superposition of the resonant modes with characteristic decay factors seems a valuable method of the analysis of the signal, since it offers high reduction of the data to the few parameters of a clear physiological meaning.

We have developed a system for simulating the conditions of avian surveys in which birds are identifi ed by sound. The system uses a laptop computer to control a set of amplifi ed MP3 players placed at known locations around a survey point. The system can realistically simulate a known population of songbirds under a range of factors that aff ect detection probabilities. The goals of our research are to describe the sources and range of variability aff ecting point-count estimates and to fi nd applications of sampling theory and methodologies that produce practical improvements in the quality of bird-census data. Initial experiments in an open fi eld showed that, on average, observers tend to undercount birds on unlimited-radius counts, though the proportion of birds counted by individual observers ranged from 81% to 132% of the actual total. In contrast to the unlimited-radius counts, when data were truncated at a 50-m radius around the point, observers overestimated the total population by 17% to 122%. Results also illustrate how detection distances decline and identifi cation errors increase with increasing levels of ambient noise. Overall, the proportion of birds heard by observers decreased by 28 ± 4.7% under breezy conditions, 41 ± 5.2% with the presence of additional background birds, and 42 ± 3.4% with the addition of 10 dB of white noise. These fi ndings illustrate some of the inherent diffi culties in interpreting avian abundance estimates based on auditory detections, and why estimates that do not account for variations in detection probability will not withstand critical scrutiny.

The classical solution to the noise removal problem is the Wiener filter, which utilizes the second-order statistics of the Fourier decomposition. Subband decompositions of natural images have significantly non-Gaussian higher-order point statistics; these statistics capture image properties that elude Fourier-based techniques. We develop a Bayesian estimator that is a natural extension of the Wiener solution, and that exploits these higher-order statistics. The resulting nonlinear estimator performs a "coring" operation. We provide a simple model for the subband statistics, and use it to develop a semi-blind noise-removal algorithm based on a steerable wavelet pyramid.

In this paper we present a formulation of the nonlinear stochastic differential equation which allows for systematic approximations. The method is not restricted to the asymptotic, i.e., stationary, regime but can be applied to derive effective equations describing the relaxation of the system from arbitrary initial conditions. The basic idea is to reduce the nonlinear Langevin equation to an equivalent equilibrium problem, which can then be studied with the methods of conventional equilibrium statistical field theory. A particular well suited perturbative scheme is that developed in quantum field theory by Cornwall, Jackiw and Tomboulis. We apply this method to the study of N component Ginzburg-Landau equation in zero spatial dimension. In the limit of N → ∞ we can solve the effective equations and obtain closed forms for the time evolutions of the average field and of the two-time connected correlation

A crucial part of a speech recognizer is the acoustic feature extraction, especially when the application is intended to be used in noisy environment. In this paper we investigate several novel front-end techniques and compare them to multiple baselines. Recognition tests were performed on studio quality wide band recordings on Hungarian as well as on narrow band telephone speech including real-life noises collected in six languages: English, German, French, Italian, Spanish and Hungarian. The following baseline feature types were used with several settings: Mel Frequency Cepstral Coefficients (MFCC),

We present an analysis of the frequency stability degradation of an optical atomic frequency standard which is operated sequentially, and that is caused by the frequency noise of the laser used to interrogate the clock transition. This is an extension to optical frequencies of the 'Dick effect' already studied in atomic microwave frequency standards. It is shown that the simple concept of laser linewidth is not the relevant parameter to estimate the frequency stability degradation. Rather, the details of the laser frequency noise spectral density must be accounted for together with the parameters of the interrogation method. We compute the optical Dick effect in the case of a four pulse Ramsey-Bordé interferometer. We show that it may be minimized by optimizing the time sequence so that only the Fourier frequencies with minimum laser noise are sampled. Finally, we evaluate the degradation which would be obtained with one of our lasers used as an interrogation oscillator. This laser reaches a white noise floor S ν ( f ) = 10 −2 Hz 2 /Hz at a Fourier frequency of 100 Hz. We show that with this particular laser, a relative frequency stability of the order of 10 −16 in a 1 s averaging time can be reached using realistic experimental parameters.

The noise can stabilize a fluctuating or a periodically driven metastable state in such a way that the system remains in this state for a longer time than in the absence of white noise. This is the noise enhanced stability phenomenon, observed experimentally and numerically in ...

A main research topic in PWM-VSI inverter-driven electrical machines is to reduce the generated acoustic noise which often is dominated by a multiple of the switching frequency in the inverter. This paper proposes a modulation scheme for reducing the acoustic noise effect from an AC-machine which can be implemented digitally for low and high performance systems. The scheme is based on a Stator-Flux Asynchronous Vector Modulation (SFAVM) imposed by a digital band limited PWM white noise generator for varying the switching frequency randomly. The white noise generator can be used for 8-, 16and 32-bit microcontrollers. The modulation strategy is tested in a 1 kVA high performance 16-bit microprocessor controlled ac-drive system. Voltage-spectra on the line-to-line voltage and the acoustic noise spectra are presented and show that the new modulation strategy can decrease the noise effect. The stator-fluxpolygon and the line current are measured and demonstrate the random modulation strategy. Fmally, the total sound pressure level from the ac-machine is investigated with fixed switching frequencies and with different randomly modulated frequency spans. It is concluded that a properly chosen fixed switching frequency has the lowest total sound pressure level. However, the random modulation strategy distributes the noise frequencies and the noise is more comfortable and less annoying.

Oscillators are key components of electronic systems. Undesired perturbations, i.e. noise, in practical electronic systems adversely affect the spectral and timing properties of oscillators resulting in phase noise, which is a key performance limiting factor, being a major contributor to bit-error-rate (BER) of RF communication systems, and creating synchronization problems in clocked and sampled-data systems. In this paper, we first present a theory and numerical methods for nonlinear perturbation and noise analysis of oscillators described by a system of differential-algebraic equations (DAEs), which extends our recent results on perturbation analysis of autonomous ordinary differential equations (ODEs). In developing the above theory, we rely on novel results we establish for linear periodically time-varying (LPTV) systems: Floquet theory for DAEs. We then use this nonlinear perturbation analysis to derive the stochastic characterization, including the resulting oscillator spectrum, of phase noise in oscillators due to colored (e.g., 1= f noise), as opposed to white, noise sources. The case of white noise sources has already been treated by us in a recent publication. The results of the theory developed in this work enabled us to implement a rigorous and effective analysis and design tool in a circuit simulator for low phase noise oscillator design.

Abstruct-We introduce a computationally efficient recursive i m p~e~e n~a~i o n of digital finite impulse response (FIR) filters for e s~i~a~~n g the rate of change or slope of digitized signals, The proposed FIR differentiator is characterized by the optimal attenuation of white noise and an efficient suppression of upperband frequencies. The basic structure needs only one multiplier, which becomes a power of two with an appropriate selection of the length of the impulse response. The structure does not need resetting and recovers from any bit errors. For long filters, sampling rate reduction by decimation gives further computational savings.

Abstmt-A new algorithm is presented for adaptive notch filtering and parametric spectral estimation of multiple narrow-band or sine wave signals in an additive broad-band process. The algorithm is of recursive prediction error (RPE) form and uses a special constrained model of infinite impulse response (IIR) with a minimal number of parameters. The convergent fdter is characterized by highly narrow bandwidth and uniform notches of desired shape. For sufficiently large data sets, the variances of the sine wave frequency estimates are of the same order of magnitude as the Cramer-Rao bound. Results from simulations illustrate the performance of the algorithm under a wide range of conditions.

The aim of this study was to investigate the effects of tinnitus on mental activity. In a mixed design study, the performance of 20 subjects with tinnitus and 20 healthy control subjects was compared on the digit-symbol test, completed in three auditory conditions: silence, masking and intermittent masking. Results showed marked overall differences between patients and controls on all three conditions. Lower scores on the digit-symbol test were observed during the intermittent masking condition compared with the masking condition for the patients. There was no difference between silence (e.g. tinnitus) and the masking condition, or between silence and the intermittent masking condition. The control subjects scored lower on the task when exposed to the intermittent masking compared to both silence and masking. The patients had higher depression and anxiety scores than the controls. These findings suggest that there is a link between masking sounds and how tinnitus affects cognitive capacity.

Purpose -The purpose of this paper is to analyze the effect of the white, colored and mixture noise perturbations as Gaussian process on the parameters of the RL electrical circuit including potential source and resistance. Design/methodology/approach -By adding different noise terms in the voltage and resistance parameters of an RL electrical circuit, the deterministic model is replaced by a stochastic differential equation (SDE). Findings -Owing to the application of multiple Ito's formula the analytical solutions of resulted SDEs have been obtained. Furthermore, based on a numerical method involving Euler-Maruyama scheme, the solution of the problem at the point of interest as a continuous time stochastic process has been obtained. Also shown is that the confidence interval for mean of solutions with colored and mixture noises is better than white noise. Practical implications -Numerical tests via Matlab programming are performed in order to show the efficiency and accuracy of the present work. Numerical experiments show that an excellent estimation on the solution can be obtained within a couple of minutes time at Pentium IV-2.4 GHz PC. Originality/value -It is believed that the stochastic model of an RL circuit with colored and mixture noises in potential source has not been studied before. Furthermore, according to latest information from the research works, two stochastic parameters in voltage and resistance of RL circuit including colored and mixture noise processes have been investigated for the first time in this paper.

In seismic retrofit of a long-span truss bridge in Japan, a new retrofit scheme was applied in which the existing bearings of the bridge were replaced by a new floor deck isolation system. The floor decks and isolation system together can be viewed as a giant tuned mass damper (TMD) to reduce the seismic force of the truss. This motivates a study on the optimal design of a TMD for a single-degree-of-freedom structure under seismic loads in this paper. Kanai-Tajimi spectrum is selected to model the earthquake excitation. It is shown that, when ratio of the characteristic ground frequency in the Kanai-Tajimi spectrum to the structural frequency is above three, the ground motion can be assumed to be a white noise to design TMD. For a smaller ground frequency ratio, simple formulas of the optimal TMD parameters are obtained. The dependence of optimal TMD parameters on mass ratio especially for large TMD is highlighted. It is found that the optimal TMD has lower tuning frequency and higher damping ratio as the mass ratio increases. For a large mass ratio, TMD becomes very effective in minimizing the primary structure response and robust against uncertainties in the parameters of the system.

There is disagreement in the literature about the importance of sleep disruption from intensive care unit (ICU) environmental noise. Previous reports have assumed that sleep disruption is produced by high-peak noise. This study aimed to determine whether peak noise or the change in noise level from baseline is more important in inducing sleep disruption. We hypothesized that white noise added to the environment would reduce arousals by reducing the magnitude of changing noise levels.Four subjects underwent polysomnography under three conditions: (1) baseline, (2) exposure to recorded ICU noise and (3) exposure to ICU noise and mixed-frequency white noise, while one additional subject completed the first two conditions. Baseline and peak noise levels were recorded for each arousal from sleep.A total of 1178 arousals were recorded during these studies. Compared to the baseline night (13.3±1.8 arousals/h) the arousal index increased during the noise (48.4±7.6) but not the white noise/ICU noise night (15.7±4.5) (P<0.004). The change in sound from baseline to peak, rather than the peak sound level, determined whether an arousal occurred and was the same for the ICU noise and white noise/ICU noise condition (17.7±0.4 versus 17.5±0.3 DB, P=0.65).Peak noise was not the main determinant of sleep disruption from ICU noise. Mixed frequency white noise increases arousal thresholds in normal individuals exposed to recorded ICU noise by reducing the difference between background noise and peak noise.

In seismic retrofit of a long-span truss bridge in Japan, a new retrofit scheme was applied in which the existing bearings of the bridge were replaced by a new floor deck isolation system. The floor decks and isolation system together can be viewed as a giant tuned mass damper (TMD) to reduce the seismic force of the truss. This motivates a study on the optimal design of a TMD for a single-degree-of-freedom structure under seismic loads in this paper. Kanai-Tajimi spectrum is selected to model the earthquake excitation. It is shown that, when ratio of the characteristic ground frequency in the Kanai-Tajimi spectrum to the structural frequency is above three, the ground motion can be assumed to be a white noise to design TMD. For a smaller ground frequency ratio, simple formulas of the optimal TMD parameters are obtained. The dependence of optimal TMD parameters on mass ratio especially for large TMD is highlighted. It is found that the optimal TMD has lower tuning frequency and higher damping ratio as the mass ratio increases. For a large mass ratio, TMD becomes very effective in minimizing the primary structure response and robust against uncertainties in the parameters of the system.

The diffusion equation is solved under stochastic nonhomogeneity using eigen function expansion and the Georges method. The statistical moments of the solution process are computed through the two previously mentioned techniques and proved to be the same. A general solution is obtained under general initial and boundary conditions. A random source composed of deterministic and stochastic parts is taken into consideration. The stochastic part is then restricted to a generalized Gaussian field, mainly modulated white noise. A special case is considered under constant noise level and constant average noise. A numerical case study concerning pollution in a stream is solved and a parametric study is achieved through various figures. ᮊ

A three-stimulus auditory oddball series was presented to experienced Vipassana meditators during meditation and a control thought period to elicit event-related brain potentials (ERPs) in the two different mental states. The stimuli consisted of a frequent standard tone (500 Hz), an infrequent oddball tone (1000 Hz), and an infrequent distracter (white noise), with all stimuli passively presented through headphones and no task imposed. The strongest meditation compared to control state effects occurred for the distracter stimuli: N1 amplitude from the distracter was reduced frontally during meditation; P2 amplitude from both the distracter and oddball stimuli were somewhat reduced during meditation; P3a amplitude from the distracter was reduced during meditation. The meditation-induced reduction in P3a amplitude was strongest in participants reporting more hours of daily meditation practice and was not evident in participants reporting drowsiness during their experimental meditative session. The findings suggest that meditation state can decrease the amplitude of neurophysiologic processes that subserve attentional engagement elicited by unexpected and distracting stimuli. Consistent with the aim of Vipassana meditation to reduce cognitive and emotional reactivity, the state effect of reduced P3a amplitude to distracting stimuli reflects decreased automated reactivity and evaluative processing of task irrelevant attention-demanding stimuli.

This book describes the essential tools and techniques of statistical signal processing. At every stage theoretical ideas are linked to specific applications in communications and signal processing using a range of carefully chosen examples. The book begins with a development of basic probability, random objects, expectation, and second-order moment theory followed by a wide variety of examples of the most popular random process models and their basic uses and properties. Specific applications to the analysis of random signals and systems for communicating, estimating, detecting, modulating, and other processing of signals are interspersed throughout the book. Hundreds of homework problems are included and the book is ideal for graduate students of electrical engineering and applied mathematics. It is also a useful reference for researchers in signal processing and communications.

The present paper analyzes the concept of fear of death in Don DeLillo's novels White Noise and Cosmopolis, emphasizing the representations of this feeling in relation to television and economic life, respectively. While the Gladney family subconsciously attempted to escape the linear progression of time towards death by gathering in front of the TV set every Friday night, Eric Parker sought to overcome the fear of death by means of the accumulation of material possessions, as well as prestige. DeLillo's novel White Noise is a novel caught up in the web spun by the global economic features of late postmodernism, while underlining the effects of mass media on the everyday lives of American characters living in the fictional town of Blacksmith. Cosmopolis, published in 2003, was written after the tragic events of 9/11. However, it is not the story of a national catastrophy, but of a personal tragedy, the death of a 28 year old millionaire called Eric Parker. If in White Noise one infers the centrality of television to the American characters' lives, in Cosmopolis, the reader is provided with an economic outlook on the world. The consequence of the economic phenomenon on literary aesthetics is that globalized economy dominates aesthetic production. Materially wealthy, but spiritually vacuous, Eric Parker exemplifies modern decadence, whose finality is death itself.

Since independence in 1971, Bangladesh has achieved considerable economic development. With the growth of technology in Bangladesh, the Dhaka stock exchange has become accessible to common people in addition to traditional brokers: the involvement of non-professional Bangladeshis in the Dhaka share market has increased in the past several years. The Dhaka stock exchange generates reports on the latest DSE index, top gainer companies, top loser companies and monthly reviews on the Dhaka stock market, thereby enabling people to invest in the market more readily. In this paper, we have identified ARIMA (2, 1, 0) model as the best one to forecast the month ended General index of Dhaka Stock Exchange, Bangladesh. Monthly General Index of Dhaka Stock Exchange (DSE) from the Fiscal year January 31'1996 to July 31'2010 is used for this paper. We have also found that the GARCH (1, 1) model a specified set of parameters is the best fit for our concerned data set.

The total least squares (TLS) technique is a generalized least squares method to solve an overdetermined set of equations whose coefficients are noisy. The constrained total least squares (CTLS) method is a natural extension of TLS to the case when the noise components of the coefficients are algebraically related. The CTLS technique is developed here and some of its applications to superresolution harmonic analysis are presented.

We consider the asymptotic behavior of posterior distributions and Bayes estimators based on observations which are required to be neither independent nor identically distributed. We give general results on the rate of convergence of the posterior measure relative to distances derived from a testing criterion. We then specialize our results to independent, nonidentically distributed observations, Markov processes, stationary Gaussian time series and the white noise model. We apply our general results to several examples of infinite-dimensional statistical models including nonparametric regression with normal errors, binary regression, Poisson regression, an interval censoring model, Whittle estimation of the spectral density of a time series and a nonlinear autoregressive model. POSTERIOR CONVERGENCE RATES 193 dressed by Amewou-Atisso, Ghosal, Ghosh and Ramamoorthi [1] and Choudhuri, Ghosal and Roy . The main purpose of the present paper is to obtain a theorem on rates of convergence of posterior distributions in a general framework not restricted to the setup of i.i.d. observations. We specialize this theorem to several classes of non-i.i.d. models including i.n.i.d. observations, Gaussian time series, Markov processes and the white noise model. The theorem applies in every situation where it is possible to test the true parameter versus balls of alternatives with exponential error probabilities and it is not restricted to any particular structure on the joint distribution. The existence of such tests has been proven in many special cases by Le Cam and Birgé , who used them to construct estimators with optimal rates of convergence, determined by the (local) metric entropy or "Le Cam dimension" of the model. Our main theorem uses the same metric entropy measure of the complexity of the model and combines this with a measure of prior concentration around the true parameter to obtain a bound on the posterior rate of convergence, generalizing the corresponding result of Ghosal, Ghosh and van der Vaart . We apply these results to obtain posterior convergence rates for linear regression, nonparametric regression, binary regression, Poisson regression, interval censoring, spectral density estimation and nonlinear autoregression. van der Meulen, van der Vaart and van Zanten have extended the approach of this paper to several types of diffusion models.

We are interested in stationary "fluid" random evolutions with independent increments. Under some mild assumptions, we show they are solutions of a stochastic differential equation (SDE). There are situations where these evolutions are not described by flows of diffeomorphisms, but by coalescing flows or by flows of probability kernels.