Harnack Inequalities for SDEs Driven by Time-Changed Fractional Brownian Motions

Abstract

We establish Harnack inequalities for stochastic differential equations (SDEs) driven by a time-changed fractional Brownian motion with Hurst parameter $H\in (0,1/2)$. The Harnack inequality is dimension-free if the SDE has a drift which satisfies a one-sided Lipschitz condition, otherwise we still get Harnack-type estimates, but the constants will, in general, depend on the space dimension. Our proof is based on a coupling argument and a regularization argument for the time-change.

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• On Shift Harnack Inequalities for Subordinate Semigroups and Moment Estimates for Lévy Processes
• Harnack Type Inequalities and Applications for SDE Driven by Fractional Brownian Motion
• Large deviations for local time fractional Brownian motion and applications