Zeitschrift für Analysis und ihre Anwendungen
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Published online: 1998-09-30
Approximation of Stochastic Differential Equations with Modified Fractional Brownian MotionWilfried Grecksch and V.V. Anh (1) Universität Halle-Wittenberg, Germany
(2) Queensland University of Technology, Brisbane, Australia
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 $\epsilon$-optimal controls for a stochastic control problem is also given.
Keywords: Modified fractional Brownian motion, splitting method, stochastic integral, $\epsilon$-optimal control
Grecksch Wilfried, Anh V.V.: Approximation of Stochastic Differential Equations with Modified Fractional Brownian Motion. Z. Anal. Anwend. 17 (1998), 715-727. doi: 10.4171/ZAA/846