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Stochastic representation of fractional Bessel-Riesz motion

Author

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

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.

Suggested Citation

  • Anh, V.V. & Leonenko, N.N. & Sikorskii, A., 2017. "Stochastic representation of fractional Bessel-Riesz motion," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 135-139.
    • Handle: RePEc:eee:chsofr:v:102:y:2017:i:c:p:135-139
    DOI: 10.1016/j.chaos.2017.04.039
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    References listed on IDEAS

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    1. Janczura, Joanna & Wyłomańska, Agnieszka, 2009. "Subdynamics of financial data from fractional Fokker-Planck equation," MPRA Paper 30649, University Library of Munich, Germany.
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    Cited by:

    1. Luisa Beghin & Roberto Garra, 2019. "A Note on the Generalized Relativistic Diffusion Equation," Mathematics, MDPI, vol. 7(11), pages 1-9, October.

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