Infinite Dimensional Analysis, Quantum Probability and Related Topics, 2000
Soit [Formula: see text] une fonction caractéristique définie sur un Fréchet nucléaire réel X. Si... more Soit [Formula: see text] une fonction caractéristique définie sur un Fréchet nucléaire réel X. Si on suppose que [Formula: see text] est prolongeable par analycité au complexifié N de…
ABSTRACT In this work we study partial differential operators of infinite order on spaces of enti... more ABSTRACT In this work we study partial differential operators of infinite order on spaces of entire functions, generalizing some of the results presented in [2] and [5] to the new spaces introduced in [3].
1 Introduction and statement of the results Self intersection local time of Brownian motion have ... more 1 Introduction and statement of the results Self intersection local time of Brownian motion have been the subject of numerous studies of half a century. This was, in part, motivated by the important role played by self intersection local time in the construction of certain Euclidean quantum fields, see for instance [8][22][23][27]. The expres-
Self intersection local time of Brownian motion have been the subject of numerous studies of half... more Self intersection local time of Brownian motion have been the subject of numerous studies of half a century. This was, in part, motivated by the important role played by self intersection local time in the construction of certain Euclidean quantum fields, see for instance [8][22][23][27]. The expression of self intersection local time appears also in the study of polymers, see Edwards [10]. Using a chaos expansion in terms of Malliavin’s calculus or, even more appropriately white noise calculus, many results were proven see for instance [4][11][14]. More precisely it was shown in [24] that the selfintersection local time of d-dimensional Brownian motion, renormalized by subtracting some terms in its chaos expansion, was a Hida distribution, we also point out [13][19].
In this paper we are interested in polynomial interpolation of irregular functions namely those e... more In this paper we are interested in polynomial interpolation of irregular functions namely those elements of L(R, μ) for μ a given probability measure. This is of course doesn’t make any sense unless for L functions that, at least, admit a continuous version. To characterize those functions we have, first, constructed, in an abstract fashion, a chain of Sobolev like subspaces of a given Hilbert space H0. Then we have proved that the chain of Sobolev like subspaces controls the existence of a continuous version for L functions and gives a pointwise polynomial approximation with a quite accurate error estimation.
International Journal of Statistics and Probability
In this paper we are interested in approximating the conditional expectation of a given random va... more In this paper we are interested in approximating the conditional expectation of a given random variable X with respect to the standard normal distribution N(0, 1). Actually we have shown that the conditional expectation E(X|Z) could be interpolated by an N degree polynomial function of Z, φN(Z) where N is the number of observations recorded for the conditional expectation E(X|Z = z). A pointwise error estimation has been proved under reasonable condition on the random variable X.
In this paper, we introduce a class of bivariate means generated by an integral of a continuous i... more In this paper, we introduce a class of bivariate means generated by an integral of a continuous increasing function on (0, +∞). This class of means widens the spectrum of possible means and leads to many easy and interesting mean-inequalities. We show that this class of means characterizes the large class of homogeneous symmetric monotone means.
Proceedings of the International Conference on Stochastic Analysis and Applications, 2004
Given that each term of the multiple Wiener integral expansion for the renormalized self-intersec... more Given that each term of the multiple Wiener integral expansion for the renormalized self-intersection local time of higher dimensional Brownian motion converges in law to another, independent Brownian motion we resum the leading, martingale parts of these terms in closed form and also represent this sum as a stochastic integral.
In this paper we are interested in polynomial interpolation of irregular functions namely those e... more In this paper we are interested in polynomial interpolation of irregular functions namely those elements of L 2 (R, µ) for µ a given probability measure. This is of course doesn't make any sense unless for L 2 functions that, at least, admit a continuous version. To characterize those functions we have, first, constructed, in an abstract fashion , a chain of Sobolev like subspaces of a given Hilbert space H 0. Then we have proved that the chain of Sobolev like subspaces controls the existence of a continuous version for L 2 functions and gives a pointwise polynomial approximation with a quite accurate error estimation.
Infinite Dimensional Analysis, Quantum Probability and Related Topics, 2000
Soit [Formula: see text] une fonction caractéristique définie sur un Fréchet nucléaire réel X. Si... more Soit [Formula: see text] une fonction caractéristique définie sur un Fréchet nucléaire réel X. Si on suppose que [Formula: see text] est prolongeable par analycité au complexifié N de…
ABSTRACT In this work we study partial differential operators of infinite order on spaces of enti... more ABSTRACT In this work we study partial differential operators of infinite order on spaces of entire functions, generalizing some of the results presented in [2] and [5] to the new spaces introduced in [3].
1 Introduction and statement of the results Self intersection local time of Brownian motion have ... more 1 Introduction and statement of the results Self intersection local time of Brownian motion have been the subject of numerous studies of half a century. This was, in part, motivated by the important role played by self intersection local time in the construction of certain Euclidean quantum fields, see for instance [8][22][23][27]. The expres-
Self intersection local time of Brownian motion have been the subject of numerous studies of half... more Self intersection local time of Brownian motion have been the subject of numerous studies of half a century. This was, in part, motivated by the important role played by self intersection local time in the construction of certain Euclidean quantum fields, see for instance [8][22][23][27]. The expression of self intersection local time appears also in the study of polymers, see Edwards [10]. Using a chaos expansion in terms of Malliavin’s calculus or, even more appropriately white noise calculus, many results were proven see for instance [4][11][14]. More precisely it was shown in [24] that the selfintersection local time of d-dimensional Brownian motion, renormalized by subtracting some terms in its chaos expansion, was a Hida distribution, we also point out [13][19].
In this paper we are interested in polynomial interpolation of irregular functions namely those e... more In this paper we are interested in polynomial interpolation of irregular functions namely those elements of L(R, μ) for μ a given probability measure. This is of course doesn’t make any sense unless for L functions that, at least, admit a continuous version. To characterize those functions we have, first, constructed, in an abstract fashion, a chain of Sobolev like subspaces of a given Hilbert space H0. Then we have proved that the chain of Sobolev like subspaces controls the existence of a continuous version for L functions and gives a pointwise polynomial approximation with a quite accurate error estimation.
International Journal of Statistics and Probability
In this paper we are interested in approximating the conditional expectation of a given random va... more In this paper we are interested in approximating the conditional expectation of a given random variable X with respect to the standard normal distribution N(0, 1). Actually we have shown that the conditional expectation E(X|Z) could be interpolated by an N degree polynomial function of Z, φN(Z) where N is the number of observations recorded for the conditional expectation E(X|Z = z). A pointwise error estimation has been proved under reasonable condition on the random variable X.
In this paper, we introduce a class of bivariate means generated by an integral of a continuous i... more In this paper, we introduce a class of bivariate means generated by an integral of a continuous increasing function on (0, +∞). This class of means widens the spectrum of possible means and leads to many easy and interesting mean-inequalities. We show that this class of means characterizes the large class of homogeneous symmetric monotone means.
Proceedings of the International Conference on Stochastic Analysis and Applications, 2004
Given that each term of the multiple Wiener integral expansion for the renormalized self-intersec... more Given that each term of the multiple Wiener integral expansion for the renormalized self-intersection local time of higher dimensional Brownian motion converges in law to another, independent Brownian motion we resum the leading, martingale parts of these terms in closed form and also represent this sum as a stochastic integral.
In this paper we are interested in polynomial interpolation of irregular functions namely those e... more In this paper we are interested in polynomial interpolation of irregular functions namely those elements of L 2 (R, µ) for µ a given probability measure. This is of course doesn't make any sense unless for L 2 functions that, at least, admit a continuous version. To characterize those functions we have, first, constructed, in an abstract fashion , a chain of Sobolev like subspaces of a given Hilbert space H 0. Then we have proved that the chain of Sobolev like subspaces controls the existence of a continuous version for L 2 functions and gives a pointwise polynomial approximation with a quite accurate error estimation.
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