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Zeitschrift für Analysis und ihre Anwendungen


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Volume 17, Issue 3, 1998, pp. 715–727
DOI: 10.4171/ZAA/846

Published online: 1998-09-30

Approximation of Stochastic Differential Equations with Modified Fractional Brownian Motion

Wilfried Grecksch[1] and V.V. Anh[2]

(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