The 𝒮-Transform of Sub-fBm and an Application to a Class of Linear Subfractional BSDEs

Abstract

Let SH be a subfractional Brownian motion with index 0<H<1. Based on the 𝒮-transform in white noise analysis we study the stochastic integral with respect to SH, and we also prove a Girsanov theorem and derive an Itô formula. As an application we study the solutions of backward stochastic differential equations driven by SH of the form -dYt=f(t,Yt,Zt)dt-ZtdStH, t∈[0,T],YT=ξ, where the stochastic integral used in the above equation is Pettis integral. We obtain the explicit solutions of this class of equations under suitable assumptions.