Correlated continuous time random walks and fractional Pearson diffusions

Leonenko, Nikolai ORCID: https://orcid.org/0000-0003-1932-4091, Papic, Ivan, Sikorski, Alla and Suvak, Nenad 2018. Correlated continuous time random walks and fractional Pearson diffusions. Bernoulli 24 (4B) , pp. 3603-3627. 10.3150/17-BEJ972

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Abstract

Continuous time random walks have random waiting times between particle jumps. We define the correlated continuous time random walks (CTRWs) that converge to fractional Pearson diffusions (fPDs). The jumps in these CTRWs are obtained from Markov chains through the Bernoulli urn-scheme model and Wright-Fisher model. The jumps are correlated so that the limiting processes are not Lévy but diffusion processes with non-independent increments. The waiting times are selected from the domain of attraction of a stable law.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Subjects:	Q Science > QA Mathematics
Publisher:	Bernoulli Society for Mathematical Statistics and Probability
ISSN:	1350-7265
Date of First Compliant Deposit:	13 July 2017
Date of Acceptance:	12 July 2017
Last Modified:	13 Nov 2024 23:30
URI:	https://orca.cardiff.ac.uk/id/eprint/102369

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