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

TL;DR

This paper proves an asymptotic log-Harnack inequality for complex stochastic differential equations with path and distribution dependence, including Dini continuous drifts, advancing the theoretical understanding of such systems.

Contribution

It introduces a novel asymptotic log-Harnack inequality applicable to path-distribution dependent SDEs with infinite memory and Dini drifts, even in the distribution-independent case.

Findings

Established a new asymptotic log-Harnack inequality for complex SDEs

Extended the inequality to include Dini continuous drifts

Applicable to SDEs with infinite memory and path dependence

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.