Derivative formulas and applications for degenerate SDEs with fractional noises

TL;DR

This paper develops derivative formulas for degenerate SDEs driven by fractional Brownian motions with H>1/2, using Malliavin calculus and coupling, and explores their applications to inequalities and hyperboundedness.

Contribution

It introduces new derivative formulas for degenerate SDEs with fractional noise and compares two different approaches, expanding the theoretical understanding of such systems.

Findings

Established derivative formulas using Malliavin calculus and coupling.

Derived (log) Harnack inequalities for the systems.

Proved hyperbounded property for the solutions.

Abstract

For degenerate stochastic differential equations driven by fractional Brownian motions with Hurst parameter $H>1/2$, the derivative formulas are established by using Malliavin calculus and coupling method, respectively. Furthermore, we find some relation between these two approaches. As applications, the (log) Harnack inequalities and the hyperbounded property are presented.