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ON SPECTRAL SIMULATION OF FRACTIONAL BROWNIAN MOTION

Published online by Cambridge University Press:  06 June 2003

A.B. Dieker
Affiliation:
CWI, 1090 GB Amsterdam, The Netherlands, and University of Twente, Faculty of Mathematical Sciences, 7500 AE Enschede, The Netherlands, E-mail: Ton.Dieker@cwi.nl
M. Mandjes
Affiliation:
CWI, 1090 GB Amsterdam, The Netherlands, and University of Twente, Faculty of Mathematical Sciences, 7500 AE Enschede, The Netherlands, E-mail: Michel.Mandjes@cwi.nl

Abstract

This article focuses on simulating fractional Brownian motion (fBm). Despite the availability of several exact simulation methods, attention has been paid to approximate simulation (i.e., the output is approximately fBm), particularly because of possible time savings. In this article, we study the class of approximate methods that are based on the spectral properties of fBm's stationary incremental process, usually called fractional Gaussian noise (fGn). The main contribution is a proof of asymptotical exactness (in a sense that is made precise) of these spectral methods. Moreover, we establish the connection between the spectral simulation approach and a widely used method, originally proposed by Paxson, that lacked a formal mathematical justification. The insights enable us to evaluate the Paxson method in more detail. It is also shown that spectral simulation is related to the fastest known exact method.

Type
Research Article
Copyright
© 2003 Cambridge University Press

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