English

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

Probability 2023-07-10 v2

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.

Keywords

Cite

@article{arxiv.2209.14619,
  title  = {Regularities and Exponential Ergodicity in Entropy for SDEs Driven by Distribution Dependent Noise},
  author = {Xing Huang and Feng-Yu Wang},
  journal= {arXiv preprint arXiv:2209.14619},
  year   = {2023}
}

Comments

23 pages

R2 v1 2026-06-28T02:21:07.142Z