CAUCHY PROBLEM OF STOCHASTIC KINETIC EQUATIONS

Xiaolong Zhang; Xicheng Zhang

doi:10.1214/23-AAP1961

CAUCHY PROBLEM OF STOCHASTIC KINETIC EQUATIONS

Xiaolong Zhang, Xicheng Zhang

School of Mathematics and Statistics

Beijing Institute of Technology

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

In this paper we establish the optimal regularity estimates for the Cauchy problem of stochastic kinetic equations with random coefficients in anisotropic Besov spaces. As applications, we study the nonlinear filtering problem for a degenerate diffusion process, and obtain the existence and regularity of conditional probability densities under a few assumptions. Moreover, we also show the well-posedness for a class of super-linear growth stochastic kinetic equations driven by velocity-time white noises.

Original language	English
Pages (from-to)	148-202
Number of pages	55
Journal	Annals of Applied Probability
Volume	34
Issue number	1A
DOIs	https://doi.org/10.1214/23-AAP1961
Publication status	Published - Feb 2024

Keywords

Anisotropic Besov spaces
Itô–Wentzell’s formula
Stochastic kinetic equations
filtering problem

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Zhang, X., & Zhang, X. (2024). CAUCHY PROBLEM OF STOCHASTIC KINETIC EQUATIONS. Annals of Applied Probability, 34(1A), 148-202. https://doi.org/10.1214/23-AAP1961

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keywords = "Anisotropic Besov spaces, It{\^o}–Wentzell{\textquoteright}s formula, Stochastic kinetic equations, filtering problem",

author = "Xiaolong Zhang and Xicheng Zhang",

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N2 - In this paper we establish the optimal regularity estimates for the Cauchy problem of stochastic kinetic equations with random coefficients in anisotropic Besov spaces. As applications, we study the nonlinear filtering problem for a degenerate diffusion process, and obtain the existence and regularity of conditional probability densities under a few assumptions. Moreover, we also show the well-posedness for a class of super-linear growth stochastic kinetic equations driven by velocity-time white noises.

AB - In this paper we establish the optimal regularity estimates for the Cauchy problem of stochastic kinetic equations with random coefficients in anisotropic Besov spaces. As applications, we study the nonlinear filtering problem for a degenerate diffusion process, and obtain the existence and regularity of conditional probability densities under a few assumptions. Moreover, we also show the well-posedness for a class of super-linear growth stochastic kinetic equations driven by velocity-time white noises.

KW - Anisotropic Besov spaces

KW - Itô–Wentzell’s formula

KW - Stochastic kinetic equations

KW - filtering problem

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JO - Annals of Applied Probability

JF - Annals of Applied Probability

IS - 1A

ER -

CAUCHY PROBLEM OF STOCHASTIC KINETIC EQUATIONS

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Keywords

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