Harnack Type Inequalities and Applications for SDE Driven by Fractional Brownian Motion

Abstract

For stochastic differential equation driven by fractional Brownian motion with Hurst parameter $H>1/2$, Harnack type inequalities are established by constructing a coupling with unbounded time-dependent drift. These inequalities are applied to the study of existence and uniqueness of invariant measure for a discrete Markov semigroup constructed in terms of the distribution of the solution. Furthermore, we show that entropy-cost inequality holds for the invariant measure.

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• Harnack Type Inequalities and Applications for SDE Driven by Fractional Brownian Motion
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Cited by in corpus (9)

• Harnack Type Inequalities and Applications for SDE Driven by Fractional Brownian Motion
• Integration by parts formula and applications for SDE driven by fractional Brownian motion
• Harnack inequalities for $1$-$d$ stochastic Klein-Gordon type equations
• Bismut formulae and applications for stochastic (functional) differential equations driven by fractional Brownian motions
• Derivative formulas and applications for degenerate SDEs with fractional noises
• A Study of a Class of Stochastic Volterra Equations Driven by Fractional Brownian Motion
• Harnack Inequalities for SDEs Driven by Time-Changed Fractional Brownian Motions
• A study on the fractional Gruschin type process
• Distribution-Dependent Stochastic Functional Differential Equations