Harnack Inequalities and Applications for Stochastic Differential Equations Driven by Fractional Brownian Motion

TL;DR

This paper establishes Harnack inequalities for stochastic differential equations driven by fractional Brownian motion with Hurst parameter less than 1/2, and explores their implications for properties like strong Feller and entropy-cost inequalities.

Contribution

It introduces novel Harnack inequalities for SDEs driven by fractional Brownian motion with H<1/2, expanding the theoretical understanding of such equations.

Findings

Harnack inequalities are proved for SDEs with fractional Brownian motion (H<1/2)

Applications include establishing strong Feller property and entropy-cost inequalities

Provides new tools for analyzing stochastic equations driven by fractional Brownian motion

Abstract

In the paper, Harnack inequalities are established for stochastic differential equations driven by fractional Brownian motion with Hurst parameter $H<1/2$. As applications, strong Feller property, log-Harnack inequality and entropy-cost inequality are given.