Approximation of stochastic differential equations driven by fractional Brownian motion. (English) Zbl 1143.60320

Lisei, Hannelore; Soós, Anna

Dalang, Robert C. (ed.) et al., Seminar on stochastic analysis, random fields and applications V. Proceedings of the 5th seminar, Centro Stefano Franscini, Ascona, Switzerland, May 30 to June 3, 2005. Basel: Birkhäuser (ISBN 978-3-7643-8457-9/hbk). Progress in Probability 59, 227-241 (2008).

Summary: The aim of this paper is to approximate the solution of a stochastic differential equation driven by fractional Brownian motion (with Hurst index greater than \(\frac12\)) using a series expansion for the noise. We prove that the solution of the approximating equations converge in probability to the solution of the given equation. We illustrate the approximation through an example from mathematical finance.
For the entire collection see [Zbl 1130.60005].

MSC:

60H10	Stochastic ordinary differential equations (aspects of stochastic analysis)
60H40	White noise theory
60H05	Stochastic integrals

Keywords:

stochastic differential equations; approximation; fractional Brownian motion