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
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
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