NDLI: Spectral density of a fractional Brownian process

Content Provider	Springer Nature Link
Author	Kuleshov, E. L. Grudin, B. N.
Copyright Year	2013
Abstract	A model of a fractional Brownian process is defined by its structural function with a Hurst exponent α ∈ (0,1). It is proved that the spectral density of this process exists and coincides with the known power-law relationship only for values of the exponent α ∈ (0,1/2]. In the range of α ∈ (1/2,1), the spectral density does not exist and the periodogram estimate of the exponent has a constant value equal to 1/2. The theoretical results were verified by modeling trajectories of the process, calculating periodograms, and estimating the spectral density exponent.
Starting Page	228
Ending Page	233
Page Count	6
File Format	PDF
ISSN	87566990
Journal	Optoelectronics, Instrumentation and Data Processing
Volume Number	49
Issue Number	3
e-ISSN	19347944
Language	English
Publisher	Springer US
Publisher Date	2013-07-24
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	fractional Brownian process correlation function spectral density periodogram Optics, Optoelectronics, Plasmonics and Optical Devices
Content Type	Text
Resource Type	Article
Subject	Instrumentation Condensed Matter Physics Electrical and Electronic Engineering

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Spectral density of a fractional Brownian process