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May 2010 Approximating a geometric fractional Brownian motion and related processes via discrete Wick calculus
Christian Bender, Peter Parczewski
Bernoulli 16(2): 389-417 (May 2010). DOI: 10.3150/09-BEJ223

Abstract

We approximate the solution of some linear systems of SDEs driven by a fractional Brownian motion BH with Hurst parameter H∈(½, 1) in the Wick–Itô sense, including a geometric fractional Brownian motion. To this end, we apply a Donsker-type approximation of the fractional Brownian motion by disturbed binary random walks due to Sottinen. Moreover, we replace the rather complicated Wick products by their discrete counterpart, acting on the binary variables, in the corresponding systems of Wick difference equations. As the solutions of the SDEs admit series representations in terms of Wick powers, a key to the proof of our Euler scheme is an approximation of the Hermite recursion formula for the Wick powers of BH.

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Christian Bender. Peter Parczewski. "Approximating a geometric fractional Brownian motion and related processes via discrete Wick calculus." Bernoulli 16 (2) 389 - 417, May 2010. https://doi.org/10.3150/09-BEJ223

Information

Published: May 2010
First available in Project Euclid: 25 May 2010

zbMATH: 1248.60044
MathSciNet: MR2668907
Digital Object Identifier: 10.3150/09-BEJ223

Rights: Copyright © 2010 Bernoulli Society for Mathematical Statistics and Probability

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Vol.16 • No. 2 • May 2010
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