Approximation of Stochastic Differential Equations with Modified Fractional Brownian Motion

Abstract

The modified fractional Brownian motion is a special semimartingale. This stochastic process is suitable for studying the phenomenon of long-range dependence in a wide range of fields. This paper introduces stochastic differential equations with respect to modified fractional Brownian motion. The solution of these equations is approximated by a splitting method whose convergence in probability is proved. An application of this method to determine $ϵ$-optimal controls for a stochastic control problem is also given.