Conditional stochastic differential equations driven by fractional Brownian motion

Abstract

The aim of this paper is to analyse a WIS-stochastic differential equation driven by fractional Brownian motion with $H>\tfrac{1}{2}$. For this, we summarise the theory of fractional white noise and prove a fundamental $L^2$-estimate for WIS-integrals. We apply this to prove the existence and uniqueness of a solution in $L^2(P)$ of a conditional WIS-stochastic differential equation driven by a fractional Brownian motion with $H>\tfrac{1}{2}$ under Lipschitz conditions on its coefficients.