Bismut formulae and applications for stochastic (functional) differential equations driven by fractional Brownian motions

TL;DR

This paper derives Bismut formulae for stochastic differential equations driven by fractional Brownian motions using Malliavin calculus, enabling new inequalities and properties relevant for stochastic analysis.

Contribution

It introduces Bismut derivative formulae for fractional Brownian motion-driven equations, expanding Malliavin calculus applications in this context.

Findings

Established Bismut formulae for fractional Brownian motion equations

Derived Harnack inequalities for these equations

Proved strong Feller property for solutions

Abstract

By using Malliavin calculus, Bismut derivative formulae are established for a class of stochastic (functional) differential equations driven by fractional Brownian motions. As applications, Harnack type inequalities and strong Feller property are presented.