Regularities for distribution dependent SDEs with fractional noises

Xiliang Fan; Xing Huang; Zewei Ling

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arXiv · 2304.00768

Regularities for distribution dependent SDEs with fractional noises

Xiliang Fan·Xing Huang·Zewei Ling

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Abstract

In this paper, we investigate the regularities for a class of distribution dependent SDEs driven by two independent fractional noises $B^H$ and $\ti B^{\ti H}$ with Hurst parameters $H\in(0,1)$ and $\ti H\in(1/2,1)$. We establish the log-Harnack inequalities and Bismut formulas for the Lions derivative to this type of equations with distribution dependent noise, in both non-degenerate and degenerate cases. Our proofs consist of utilizing coupling arguments which are indeed backward couplings introduced by F.-Y. Wang \cite{Wang12b}, together with a careful analysis of fractional derivative operator.

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Xiliang Fan, Xing Huang, Zewei Ling. 2023-04-03. Regularities for distribution dependent SDEs with fractional noises. https://arxiv.org/abs/2304.00768

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