Correlation Properties of (Discrete) Fractional Gaussian Noise and Fractional Brownian Motion
Author
Source
Mathematical Problems in Engineering
Issue
Vol. 2015, Issue 2015 (31 Dec. 2015), pp.1-7, 7 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2015-08-11
Country of Publication
Egypt
No. of Pages
7
Main Subjects
Abstract EN
The fractional Gaussian noise/fractional Brownian motion framework (fGn/fBm) has been widely used for modeling and interpreting physiological and behavioral data.
The concept of 1/f noise, reflecting a kind of optimal complexity in the underlying systems, is of central interest in this approach.
It is generally considered that fGn and fBm represent a continuum, punctuated by the boundary of “ideal” 1/f noise.
In the present paper, we focus on the correlation properties of discrete-time versions of these processes (dfGn and dfBm).
We especially derive a new analytical expression of the autocorrelation function (ACF) of dfBm.
We analyze the limit behavior of dfGn and dfBm when they approach their upper and lower limits, respectively.
We show that, as H approaches 1, the ACF of dfGn tends towards 1 at all lags, suggesting that dfGn series tend towards straight line.
Conversely, as H approaches 0, the ACF of dfBm tends towards 0 at all lags, suggesting that dfBm series tend towards white noise.
These results reveal a severe breakdown of correlation properties around the 1/f boundary and challenge the idea of a smooth transition between dfGn and dfBm processes.
We discuss the implications of these findings for the application of the dfGn/dfBm model to experimental series, in terms of theoretical interpretation and modeling.
American Psychological Association (APA)
Delignières, Didier. 2015. Correlation Properties of (Discrete) Fractional Gaussian Noise and Fractional Brownian Motion. Mathematical Problems in Engineering،Vol. 2015, no. 2015, pp.1-7.
https://search.emarefa.net/detail/BIM-1073944
Modern Language Association (MLA)
Delignières, Didier. Correlation Properties of (Discrete) Fractional Gaussian Noise and Fractional Brownian Motion. Mathematical Problems in Engineering No. 2015 (2015), pp.1-7.
https://search.emarefa.net/detail/BIM-1073944
American Medical Association (AMA)
Delignières, Didier. Correlation Properties of (Discrete) Fractional Gaussian Noise and Fractional Brownian Motion. Mathematical Problems in Engineering. 2015. Vol. 2015, no. 2015, pp.1-7.
https://search.emarefa.net/detail/BIM-1073944
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1073944