Derivative Formula and Harnack Inequality for Degenerate Functional SDEs

TL;DR

This paper develops new mathematical tools like derivative formulas and Harnack inequalities for a specific class of degenerate functional stochastic differential equations, enhancing understanding of their behavior.

Contribution

It introduces coupling methods to derive gradient estimates and Harnack inequalities for degenerate functional SDEs, a novel approach in this context.

Findings

Established derivative formulas for degenerate functional SDEs

Derived gradient estimates for the associated semigroup

Proved Harnack inequalities for the class of equations

Abstract

By constructing successful couplings, the derivative formula, gradient estimates and Harnack inequalities are established for the semigroup associated with a class of degenerate functional stochastic differential equations.