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 -optimal controls for a stochastic control problem is also given.
Cite this article
Wilfried Grecksch, V.V. Anh, Approximation of Stochastic Differential Equations with Modified Fractional Brownian Motion. Z. Anal. Anwend. 17 (1998), no. 3, pp. 715–727DOI 10.4171/ZAA/846