Probability density of the complex-valued fractional Brownian motion of order \(n\) via the maximum entropy principle in \(\mathbb R_{+}^{1/n}\)
type: Item
instance of: scholarly article
title: Probability density of the complex-valued fractional Brownian motion of order \(n\) via the maximum entropy principle in \(\mathbb R_{+}^{1/n}\)
zbMATH Open document ID: 1061.60051
DOI: 10.1016/S0960-0779(03)00191-7
published in: Chaos, Solitons and Fractals
publication date: 2004-07-01T00:00:00Z
review text: Looking for probability density in the form \(p(z^n)\), where \(n\) is order of the noise, the author couverts an integral over the complex space into the sum of several integrals over the real axis, and from there, to meaningfully extend the definition of informational entropy in this new framework. Then applying the maximum entropy principle will directly yield the sought expression of the complex white noise of order \(n\). The author takes the opportunity to extend the definition of colored noise to obtain the parallel concept of coloured noise of order \(n\) and calculates its (auto)correlation function of order \(n\). As an example of application, the author considers a stability problem in which the equlilibrium position is disturbed by complex-valued noises of order \(n\).
reviewed by: Messoud Efendiev
Mathematics Subject Classification ID: 60G99
Mathematics Subject Classification ID: 60G51
Mathematics Subject Classification ID: 60J65
Mathematics Subject Classification ID: 82B31
zbMATH DE Number: 2077277
zbMATH Keywords: probability density
zbMATH Keywords: maximum entropy principles
zbMATH Keywords: white noise
zbMATH Keywords: stability
author: Guy Jumarie
MaRDI profile type: Publication
cites work: On stochasticity and turbulence in the federal funds market
cites work: Information Theory and Statistical Mechanics
cites work: Stochastic processes and filtering theory
cites work: A new approach to complex-valued fractional Brownian motion via rotating white noise
cites work: A new approach to fractional Brownian motion of order \(n\) via random walk in the complex plane
cites work: Maximum entropy, information without probability and complex fractals. Classical and quantum approach
cites work: Would dynamic systems involving human factors be necessarily of fractal nature?
cites work: Q3883962
cites work: Q5750089
cites work: Construction of a complex-valued fractional Brownian motion of order N
description: scientific article; zbMATH DE number 2077277