February 2024 Cauchy problem of stochastic kinetic equations
Xiaolong Zhang, Xicheng Zhang
Author Affiliations +
Ann. Appl. Probab. 34(1A): 148-202 (February 2024). DOI: 10.1214/23-AAP1961

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.

Funding Statement

This work is supported by NNSFC grant of China (Nos. 12131019, 11731009) and the DFG through the CRC 1283 “Taming uncertainty and profiting from randomness and low regularity in analysis, stochastics and their applications”.

Acknowledgments

The authors would like to thank Zimo Hao for his quite useful discussions, and the anonymous referees for their constructive comments.

Citation

Download Citation

Xiaolong Zhang. Xicheng Zhang. "Cauchy problem of stochastic kinetic equations." Ann. Appl. Probab. 34 (1A) 148 - 202, February 2024. https://doi.org/10.1214/23-AAP1961

Information

Received: 1 May 2021; Revised: 1 August 2022; Published: February 2024
First available in Project Euclid: 28 January 2024

MathSciNet: MR4696275
zbMATH: 07829140
Digital Object Identifier: 10.1214/23-AAP1961

Subjects:
Primary: 35R60 , 60H15

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

Rights: Copyright © 2024 Institute of Mathematical Statistics

Vol.34 • No. 1A • February 2024
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