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arXiv · 2507.09129

Asymptotic log-Harnack inequality for path-distribution dependent SDEs with infinite memory and Dini drift

Xiao-Yu Zhao
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Abstract

We establish an asymptotic log-Harnack inequality for stochastic differential equations on $\R^d$ whose coefficients depend on the path and distribution for the whole history, allowing the drift to contain a Dini continuous term. The result is new even in the distribution-independent case.

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Xiao-Yu Zhao. 2025-07-12. Asymptotic log-Harnack inequality for path-distribution dependent SDEs with infinite memory and Dini drift. https://arxiv.org/abs/2507.09129

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