Diffusive representation of N-th order fractional brownian motion

Jaka Sembiring; Kudrat Soemintapoera; Tetsunori Kobayashi; Kageo Akizuki

doi:10.1016/S1474-6670(17)34759-6

Diffusive representation of N-th order fractional brownian motion

Jaka Sembiring, Kudrat Soemintapoera, Tetsunori Kobayashi, Kageo Akizuki

School of Fundamental Science and Engineering

Research output: Contribution to journal › Conference article › peer-review

2 Citations (Scopus)

Abstract

This paper describes an effort to give a different representation of a newly Introduced n-th order fractional Brownian motion (n-fBm). The new representation is called diffusive representation which has been successfully applied to the 1/f^α fractional noise. Thus this paper generalizes such representation to cover also n-fBm which is an extension to the ordinary fBm, due to the fact that the spectral properties of n-fBm cover larger range of parameter α. Different from 1/f^α case, the solution involves finite part concept of theory of distribution. The advantage of the proposed method on synthesizing sample of n-fBm is presented.

Original language	English
Pages (from-to)	181-185
Number of pages	5
Journal	IFAC Proceedings Volumes (IFAC-PapersOnline)
Volume	36
Issue number	16
DOIs	https://doi.org/10.1016/S1474-6670(17)34759-6
Publication status	Published - 2003
Event	13th IFAC Symposium on System Identification, SYSID 2003 - Rotterdam, Netherlands Duration: 2003 Aug 27 → 2003 Aug 29

Keywords

Brownian motion
Gaussian processes
Signal processing
Stochastic systems

ASJC Scopus subject areas

Control and Systems Engineering

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10.1016/S1474-6670(17)34759-6

Cite this

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abstract = "This paper describes an effort to give a different representation of a newly Introduced n-th order fractional Brownian motion (n-fBm). The new representation is called diffusive representation which has been successfully applied to the 1/fα fractional noise. Thus this paper generalizes such representation to cover also n-fBm which is an extension to the ordinary fBm, due to the fact that the spectral properties of n-fBm cover larger range of parameter α. Different from 1/fα case, the solution involves finite part concept of theory of distribution. The advantage of the proposed method on synthesizing sample of n-fBm is presented.",

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AU - Sembiring, Jaka

AU - Soemintapoera, Kudrat

AU - Kobayashi, Tetsunori

AU - Akizuki, Kageo

PY - 2003

Y1 - 2003

N2 - This paper describes an effort to give a different representation of a newly Introduced n-th order fractional Brownian motion (n-fBm). The new representation is called diffusive representation which has been successfully applied to the 1/fα fractional noise. Thus this paper generalizes such representation to cover also n-fBm which is an extension to the ordinary fBm, due to the fact that the spectral properties of n-fBm cover larger range of parameter α. Different from 1/fα case, the solution involves finite part concept of theory of distribution. The advantage of the proposed method on synthesizing sample of n-fBm is presented.

AB - This paper describes an effort to give a different representation of a newly Introduced n-th order fractional Brownian motion (n-fBm). The new representation is called diffusive representation which has been successfully applied to the 1/fα fractional noise. Thus this paper generalizes such representation to cover also n-fBm which is an extension to the ordinary fBm, due to the fact that the spectral properties of n-fBm cover larger range of parameter α. Different from 1/fα case, the solution involves finite part concept of theory of distribution. The advantage of the proposed method on synthesizing sample of n-fBm is presented.

KW - Brownian motion

KW - Gaussian processes

KW - Signal processing

KW - Stochastic systems

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Diffusive representation of N-th order fractional brownian motion

Abstract

Keywords

ASJC Scopus subject areas

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