On spectral simulation of fractional Brownian motion

A.B. Dieker, M.R.H. Mandjes

Research output: Contribution to journalArticleAcademicpeer-review

36 Citations (Scopus)

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.
Original languageUndefined
Pages (from-to)417-434
Number of pages18
JournalProbability in the engineering and informational sciences
Volume17
Issue number3
DOIs
Publication statusPublished - Jul 2003

Keywords

  • IR-70686
  • METIS-212040
  • EWI-17749

Cite this

Dieker, A.B. ; Mandjes, M.R.H. / On spectral simulation of fractional Brownian motion. In: Probability in the engineering and informational sciences. 2003 ; Vol. 17, No. 3. pp. 417-434.
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On spectral simulation of fractional Brownian motion. / Dieker, A.B.; Mandjes, M.R.H.

In: Probability in the engineering and informational sciences, Vol. 17, No. 3, 07.2003, p. 417-434.

Research output: Contribution to journalArticleAcademicpeer-review

TY - JOUR

T1 - On spectral simulation of fractional Brownian motion

AU - Dieker, A.B.

AU - Mandjes, M.R.H.

N1 - 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.

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N2 - 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.

AB - 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.

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