Stochastic representation of fractional Bessel-Riesz motion

Anh, V. V., Leonenko, N. N. ORCID: https://orcid.org/0000-0003-1932-4091 and Sikorskii, A. 2017. Stochastic representation of fractional Bessel-Riesz motion. Chaos, Solitons and Fractals 102 , pp. 135-139. 10.1016/j.chaos.2017.04.039

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Abstract

This paper derives the stochastic solution of a Cauchy problem for the distribution of a fractional diffusion process. The governing equation involves the Bessel-Riesz derivative (in space) to model heavy tails of the distribution, and the Caputo-Djrbashian derivative (in time) to depicts the memory of the diffusion process. The solution is obtained as Brownian motion with time change in terms of the Bessel-Riesz subordinator on the inverse stable subordinator. This stochastic solution, named fractional Bessel-Riesz motion, provides a method to simulate a large class of stochastic motions with memory and heavy tails.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Subjects:	Q Science > QA Mathematics
Publisher:	Elsevier
ISSN:	0960-0779
Date of First Compliant Deposit:	17 July 2019
Date of Acceptance:	24 April 2017
Last Modified:	06 Nov 2023 21:10
URI:	https://orca.cardiff.ac.uk/id/eprint/100450

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