A new approach to complex-valued fractional Brownian motion via rotating white noise
type: Item
instance of: scholarly article
title: A new approach to complex-valued fractional Brownian motion via rotating white noise
zbMATH Open document ID: 0943.60086
DOI: 10.1016/S0960-0779(97)00173-2
published in: Chaos, Solitons and Fractals
publication date: 2000-09-04T00:00:00Z
review text: A Brownian motion of order \(n\) is defined by a probabilistic approach which is different from those of B. Mandelbrot and P. Sainty. This process is constructed in the form of the integral of a complex Gaussian white noise which itself is defined as the product of a Gaussian white noise by a complex white process which takes on values in the set of \(n\)th roots of unity. An Itô-Taylor's lemma of order \(n\) is proved allowing to derive the dynamical equations of the complex Brownian motion moments whereby a generalized Fokker-Planck equation or heat equation of order \(n\) is obtained. The framework is essentially engineering mathematics.
reviewed by: Marius Iosifescu
Mathematics Subject Classification ID: 60J65
Mathematics Subject Classification ID: 60G15
zbMATH DE Number: 1370423
zbMATH Keywords: complex-valued fractional Brownian motion
zbMATH Keywords: generalized Fokker-Planck equation
zbMATH Keywords: heat equation of order \(n\)
author: Guy Jumarie
MaRDI profile type: Publication
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Wikidata QID: Q126589642
description: scientific article; zbMATH DE number 1370423