Leonenko, Nikolai  ORCID: https://orcid.org/0000-0003-1932-4091, 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: | 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: | 01 Dec 2024 07:30 |
| URI: | https://orca.cardiff.ac.uk/id/eprint/116371 |
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