Stochastic differential equations with time-dependent coefficients driven by fractional Brownian motion

Abstract

In this paper, we study a class of stochastic differential equations with a time-dependent diffusion driven by a fractional Brownian motion with Hurst parameter 1∕2<H<1. By using a transformation formula for fractional Brownian motion, we prove the existence of weak solutions to this kind of equations under the linear growth condition, but the drift can be discontinuous. Some known results are improved.