Harnack Inequalities for Functional SDEs Driven by Subordinate Brownian Motions

TL;DR

This paper establishes Harnack inequalities for a class of functional stochastic differential equations driven by subordinate Brownian motions, extending previous results to include delay effects using coupling and approximation methods.

Contribution

It introduces new Harnack inequalities for functional SDEs with subordinate Brownian motions, incorporating delay effects with novel coupling and approximation techniques.

Findings

Harnack inequalities proven for functional SDEs with subordinate Brownian motions

Results extend to cases with delay, covering more general stochastic systems

Methodology involves coupling by change of measure and approximation techniques

Abstract

Using coupling by change of measure and an approximation technique, Wang's Harnack inequalities are established for a class of functional SDEs driven by subordinate Brownian motions. The results cover the corresponding ones in the case without delay.