On spectral simulation of fractional Brownian motion


Dieker, A.B. and Mandjes, M. (2003) On spectral simulation of fractional Brownian motion. Probability in the Engineering and Informational Sciences, 17 (3). pp. 417-434. ISSN 0269-9648

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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.
Item Type:Article
Additional information:Part of this work was done while A.B. Dieker was with the Vrije Universiteit Amsterdam. His research was supported by the Netherlands Organization for Scientific Research (NWO) under grant 631.000.002.
Copyright:© 2003 Cambridge University Press
Electrical Engineering, Mathematics and Computer Science (EEMCS)
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Link to this item:http://purl.utwente.nl/publications/70686
Official URL:https://doi.org/10.1017/S0269964803173081
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