The \(\mathcal S\)-transform of sub-fBm and an application to a class of linear subfractional BSDEs (Q2248470)

Summary: Let \(S^H\) be a subfractional Brownian motion with index \(0<H<1\). Based on the \(\mathcal S\)-transform in white noise analysis we study the stochastic integral with respect to \(S^H\), 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 \(S^H\) of the form \(-dY_t=f(t,Y_t,Z_t){dt-Z}_tdS^H_t,\;t\in[0,T],\;Y_T=\xi\), 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.