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arXiv · 2209.14619

Regularities and Exponential Ergodicity in Entropy for SDEs Driven by Distribution Dependent Noise

Xing Huang·Feng-Yu Wang
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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 application, the exponential ergodicity in entropy is investigated.

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Xing Huang, Feng-Yu Wang. 2022-09-29. Regularities and Exponential Ergodicity in Entropy for SDEs Driven by Distribution Dependent Noise. https://arxiv.org/abs/2209.14619

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