Harnack-type inequality for linear fractional stochastic equations

Abstract

Abstract Using the coupling method and Girsanov theorem, we prove a Harnack-type inequality for a stochastic differential equation with non-Lipschitz drift and driven by a fractional Brownian motion with Hurst parameter H < 1 2 {H<\frac{1}{2}} . We also investigate this inequality for a stochastic differential equation driven by an additive fractional Brownian sheet.