Stochastic representation of fractional Bessel-Riesz motion

V.V. Anh, N.N. Leonenko and A. Sikorskii

Chaos, Solitons & Fractals, 2017, vol. 102, issue C, 135-139

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.

Keywords: Bessel-Riesz Lévy motion; Bessel-Riesz subordinator; Fractional diffusion; Stochastic solution (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:102:y:2017:i:c:p:135-139

DOI: 10.1016/j.chaos.2017.04.039

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