Academia.edu no longer supports Internet Explorer.
To browse Academia.edu and the wider internet faster and more securely, please take a few seconds to upgrade your browser.
2020, arXiv: Probability
…
1 file
We consider limits for sequences of the type $\int Y_{-}df_n(X^n)$ and $[f_n(X^n)-f(X)]$ for semimartingale integrands, where $\{X^n\}_n$ either are Dirichlet processes or more generally processes admitting to quadratic variations. We here assume that the functions $\{f_n\}_n$ are either $C^1$ or absolutely continuous. We also provide important examples of how to apply this theory for sequential jump removal.
Journal of Theoretical Probability, 2012
We obtain a representation of an inhomogeneous Lévy process in a Lie group or a homogeneous space in terms of a drift, a matrix function and a measure function. Because the stochastic continuity is not assumed, our result generalizes the well known Lévy-Itô representation for stochastic continuous processes with independent increments in R d and its extension to Lie groups.
On considère un espace probabilisable (Ω, F ) que l'on appellera espace des réalisations (en anglais : sample space). Dans ce qui suit on prendra tantôt T = [0, T ] avec T > 0 ou T = [0, +∞[ que l'on identifiera comme le temps.
Journal of Functional Analysis, 2010
We derive a functional change of variable formula for non-anticipative functionals defined on the space of R d-valued right continuous paths with left limits. The functional is only required to possess certain directional derivatives, which may be computed pathwise. Our results lead to functional extensions of the Ito formula for a large class of stochastic processes, including semimartingales and Dirichlet processes. In particular, we show the stability of the class of semimartingales under certain functional transformations.
Séminaire de Probabilités XL, 2007
Lecture Notes in Mathematics, 2006
A class of stochastic processes, called "weak Dirichlet processes", is introduced and its properties are investigated in detail. This class is much larger than the class of Dirichlet processes. It is closed under C 1 -transformations and under absolutely continuous changes of measure. If a weak Dirichlet process has finite energy, as defined by Graversen and Rao, its Doob-Meyer type decomposition is unique. The methods developed here have been applied to study generalized martingale convolutions.
2021
We show that all local martingales with respect to the initially enlarged natural filtration of a vector of multivariate point processes can be weakly represented up to the minimum among the explosion times of the components. We also prove that a strong representation holds if any multivariate point process of the vector has almost surely infinite explosion time and discrete mark’s space. Then we provide a condition under which the components of the multidimensional local martingale driving the strong representation are pairwise orthogonal.
In this paper we study progressive filtration expansions with cadlag processes. Using results from the weak convergence of sigma fields theory, we first establish a semimartingale convergence theorem. Then we apply it in a filtration expansion with a process setting and provide sufficient conditions for a semimartingale of the base filtration to remain a semimartingale in the expanded filtration. Finally, an application to the expansion of a Brownian filtration with a time reversed diffusion is given through a detailed study.
Annals of the Institute of Statistical Mathematics, 2014
We consider estimation of the quadratic (co)variation of a semimartingale from discrete observations which are irregularly spaced under high-frequency asymptotics. In the univariate setting, results from Jacod (2008) are generalized to the case of irregular observations. In the two-dimensional setup under non-synchronous observations, we derive a stable central limit theorem for the estimator by Hayashi and Yoshida (2005) in the presence of jumps. We reveal how idiosyncratic and simultaneous jumps affect the asymptotic distribution. Observation times generated by Poisson processes are explicitly discussed.
2011
Using the balayage formula, we prove an inequality between the measures associated to local times of semimartingales. Our result extends the "comparison theorem of local times" of Ouknine $(1988)$, which is useful in the study of stochastic differential equations. The inequality presented in this paper covers the discontinuous case. Moreover, we study the pathwise uniqueness of some stochastic differential equations
2015
The first chapter concerns monotype population models. We first study general birth and death processes and we give non-explosion and extinction criteria, moment computations and a pathwise representation. We then show how different scales may lead to different qualitative approximations, either ODEs or SDEs. The prototypes of these equations are the logistic (deterministic) equation and the logistic Feller diffusion process. The convergence in law of the sequence of processes is proved by tightness-uniqueness argument. In these large population approximations, the competition between individuals leads to nonlinear drift terms. We then focus on models without interaction but including exceptional events due either to demographic stochasticity or to environmental stochasticity. In the first case, an individual may have a large number of offspring and we introduce the class of continuous state branching processes. In the second case, catastrophes may occur and kill a random fraction of the population and the process enjoys a quenched branching property. We emphasize on the study of the Laplace transform, which allows us to classify the long time behavior of these processes. In the second chapter, we model structured populations by measure-valued stochastic differential equations. Our approach is based on the individual dynamics. The individuals are characterized by parameters which have an influence on their survival or reproduction ability. Some of these parameters can be genetic and are inheritable except when mutations occur, but they can also be a space location or a quantity of parasites. The individuals compete for resources or other environmental constraints. We describe the population by a point measure-valued Markov process. We study macroscopic approximations of this process depending on the interplay between different scalings, and obtain in the limit either integro-differential equations or reaction-diffusion equations or nonlinear super-processes. In each case, we insist on the specific techniques for the proof of convergence and for the study of the limiting model. The limiting processes offer different models of mutation-selection dynamics. Then, we study two-level models motivated by cell division dynamics, where the cell population is discrete and characterized by a trait, which may be continuous.
ULUM 2/1 (July 2019): 133-167, 2019
Bedianashvili, G., Sagona, C., Longford, C., Martkoplishvili, I. (2019) Archaeological investigations at multi-period settlement Rabati, south-west Georgia: first preliminary results, Ancient Near Eastern Studies, 56, pp. 1-133. , 2019
Ideas Y Valores, 1980
Sociology of Health and Illness , 2024
Her Seat at the Table, 2023
The Veterinary clinics of North America. Small animal practice, 2017
Infection and immunity, 2014
Frontiers in Neurology
Arabian Journal of Chemistry, 2020
Journal of Chemical Engineering Research Updates, 2014
Molecular Cancer Therapeutics, 2019
Journal of Proteomics & Bioinformatics, 2011