A white noise approach to fractional Brownian motion

2005 ◽  
Author(s):  
David Nualart
Keyword(s):  
Brownian Motion ◽  
White Noise ◽  
Fractional Brownian Motion

A New Look at the Fractional Brownian Motion Definition

2007 ◽  
Author(s):  
Manuel Duarte Ortigueira ◽  
Arnaldo Guimara˜es Batista
Keyword(s):  
Brownian Motion ◽  
Fractional Derivative ◽  
White Noise ◽  
Fractional Brownian Motion ◽  
Fractional Derivatives ◽  
Autocorrelation Functions ◽  
Fractional Noise ◽  
Simulation Procedure ◽  
Definition Of ◽  
Fractional Noises

A reinterpretation of the classic definition of fractional Brownian motion leads to a new definition involving a fractional noise obtained as a fractional derivative of white noise. To obtain this fractional noise, two sets of fractional derivatives are considered: a) the forward and backward and b) the central derivatives. For these derivatives the autocorrelation functions of the corresponding fractional noises have the same representations. The obtained results are used to define and propose a new simulation procedure.

Effects of Noise on the Approximate Entropy of Fractional Brownian Motion Sequence

2013 ◽  
Vol 444-445 ◽  
pp. 698-702
Author(s):  
Xu Yi Hu ◽  
Li Wan ◽  
Dan Ying Xie
Keyword(s):  
Brownian Motion ◽  
White Noise ◽  
Fractional Brownian Motion ◽  
Hurst Exponent ◽  
Approximate Entropy ◽  
Poisson Noise ◽  
System Complexity ◽  
Sequence Change ◽  
Noise Type ◽  
Motion Sequence

Approximate entropy is a widely used technique to measure system complexity or regularity. In this paper, the effects of noise on the approximate entropy of fractional Brownian motion were investigated by some factors including the value of Hurst exponent, different noise type and coefficients. The results show that the values of approximate entropy of fractional Brownian motion decrease with the increase of Hurst exponent. The values increase in different degree after adding white noise in the sequence of fractional Brownian motion, and tend to be stable with the data lengthened. Meanwhile, the values of approximate entropy of mixed sequence change obviously by adding Poisson noise, while multiplying the coefficients of Poisson noise, the effects on the approximate entropy become greater.

scholarly journals Weighted Local Times of a Sub-fractional Brownian Motion as Hida Distributions

2019 ◽  
Vol 15 (2) ◽  
pp. 81 ◽  
Author(s):  
Herry Pribawanto Suryawan
Keyword(s):  
Brownian Motion ◽  
White Noise ◽  
Fractional Brownian Motion ◽  
Short Range ◽  
Probability Space ◽  
Noise Analysis ◽  
Local Times ◽  
White Noise Analysis ◽  
Self Similarity ◽  
Sample Paths

The sub-fractional Brownian motion is a Gaussian extension of the Brownian motion. It has the properties of self-similarity, continuity of the sample paths, and short-range dependence, among others. The increments of sub-fractional Brownian motion is neither independent nor stationary. In this paper we study the sub-fractional Brownian motion using a white noise analysis approach. We recall the represention of sub-fractional Brownian motion on the white noise probability space and show that Donsker's delta functional of a sub-fractional Brownian motion is a Hida distribution. As a main result, we prove the existence of the weighted local times of a $d$-dimensional sub-fractional Brownian motion as Hida distributions.

Fractional Brownian Motion and Sheet as White Noise Functionals

2006 ◽  
Vol 22 (4) ◽  
pp. 1183-1188 ◽  
Author(s):  
Zhi Yuan Huang ◽  
Chu Jin Li ◽  
Jian Ping Wan ◽  
Ying Wu
Keyword(s):  
Brownian Motion ◽  
White Noise ◽  
Fractional Brownian Motion ◽  
White Noise Functionals

scholarly journals Weighted Local Times of a Sub-fractional Brownian Motion as Hida Distributions

2020 ◽  
Vol 15 (2) ◽  
pp. 81
Author(s):  
Herry Pribawanto Suryawan
Keyword(s):  
Brownian Motion ◽  
White Noise ◽  
Fractional Brownian Motion ◽  
Short Range ◽  
Probability Space ◽  
Noise Analysis ◽  
Local Times ◽  
White Noise Analysis ◽  
Self Similarity ◽  
Sample Paths

The sub-fractional Brownian motion is a Gaussian extension of the Brownian motion. It has the properties of self-similarity, continuity of the sample paths, and short-range dependence, among others. The increments of sub-fractional Brownian motion is neither independent nor stationary. In this paper we study the sub-fractional Brownian motion using a white noise analysis approach. We recall the represention of sub-fractional Brownian motion on the white noise probability space and show that Donsker's delta functional of a sub-fractional Brownian motion is a Hida distribution. As a main result, we prove the existence of the weighted local times of a $d$-dimensional sub-fractional Brownian motion as Hida distributions.

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