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Ehrenfest-Brillouin-type correlated continuous time random walk and fractional Jacobi diffusion

Leonenko, Nikolai, Papic, I., Sikorskii, A. and Suvak, N. 2018. Ehrenfest-Brillouin-type correlated continuous time random walk and fractional Jacobi diffusion. Theory of Probability and Mathematical Statistics 2 (99) , pp. 123-133.

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Abstract

Continuous time random walks (CTRWs) have random waiting times between particle jumps. Based on Ehrenfest-Brillouin-type model motivated by economics, we define the correlated CTRW that converge to the fractional Jacobi diffusion Y (E(t)), t ≥ 0, defined as a time change of Jacobi diffusion process Y (t) to the inverse E(t) of the standard stable subordinator. In the CTRW considered in this paper, the jumps are correlated so that in the limit the outer process Y (t) is not a L´evy process but a diffusion process with non-independent increments. The waiting times between jumps are selected from the domain of attraction of a stable law, so that the correlated CTRWs with these waiting times converge to Y (E(t)).

Item Type: Article
Date Type: Publication
Status: Published
Schools: Mathematics
Publisher: American Mathematical Society
ISSN: 0094-9000
Date of First Compliant Deposit: 31 October 2018
Date of Acceptance: 29 October 2018
Last Modified: 03 Jul 2019 09:48
URI: http://orca.cf.ac.uk/id/eprint/116371

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