Harnack Inequality for Functional SDEs with Bounded Memory

TL;DR

This paper establishes a dimension-free Harnack inequality for functional SDEs with bounded memory using coupling methods, and proves the strong Feller property for the segment process, advancing the understanding of such stochastic systems.

Contribution

It introduces a coupling approach to derive Harnack inequalities for functional SDEs with bounded memory, a novel extension in the field.

Findings

Established a Harnack inequality for functional SDEs with bounded memory.

Proved the strong Feller property for the segment process.

Extended Wang's inequality to a new class of stochastic differential equations.

Abstract

We use a coupling method for functional stochastic differential equations with bounded memory to establish an analogue of Wang's dimension-free Harnack inequality \cite{MR1481127}. The strong Feller property for the corresponding segment process is also obtained.