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

Abstract

We establish an asymptotic log-Harnack inequality for stochastic differential equations on ${\mathbb{R}}^d$ 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.

21 pages