The Implicit Euler Scheme for FSDEs with Stochastic Forcing: Existence and Uniqueness of the Solution

Abstract

In this paper, we focus on fractional stochastic differential equations (FSDEs) with a stochastic forcing term, i.e., to FSDE, we add a stochastic forcing term. Using the implicit scheme of Euler’s approximation, the conditions for the existence and uniqueness of the solution of FSDEs with a stochastic forcing term are established. Such equations can be applied to considering FSDEs with a permeable wall.

Keywords

• stochastic differential equations
• stochastic forcing
• fractional Brownian motion
• implicit Euler scheme
• p-variation
• Pearson model