Abstract
As two crucial tools characterizing regularity properties of stochastic systems, the log-Harnack inequality and Bismut formula have been intensively studied for distribution dependent (McKean-Vlasov) SDEs. However, due to technical difficulties, existing results mainly focus on the case with distribution free noise. In this paper, we introduce a noise decomposition argument to establish the log-Harnack inequality and Bismut formula for SDEs with distribution dependent noise, in both non-degenerate and degenerate situations. As an application, the exponential ergodicity in entropy is investigated.
Funding Statement
The first author was supported in part by the National Key R&D Program of China (No. 2022YFA1006000) and NNSFC (12271398). The second author was supported in part by the National Key R&D Program of China (No. 2022YFA1006000, 2020YFA0712900) and NNSFC (11921001).
Acknowledgments
The authors would like to thank the editors and the referees for valuable comments and corrections.
Citation
Xing Huang. Feng-Yu Wang. "Regularities and exponential ergodicity in entropy for SDEs driven by distribution dependent noise." Bernoulli 30 (4) 3303 - 3323, November 2024. https://doi.org/10.3150/23-BEJ1715
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