Time-non-local Pearson diffusions

Ascione, Giacomo, Leonenko, Nikolai ORCID: https://orcid.org/0000-0003-1932-4091 and Pirozzi, Enrica 2021. Time-non-local Pearson diffusions. Journal of Statistical Physics 183 , 48. 10.1007/s10955-021-02786-2

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Abstract

In this paper we focus on strong solutions of some heat-like problems with a non-local derivative in time induced by a Bernstein function and an elliptic operator given by the generator or the Fokker–Planck operator of a Pearson diffusion, covering a large class of important stochastic processes. Such kind of time-non-local equations naturally arise in the treatment of particle motion in heterogeneous media. In particular, we use spectral decomposition results for the usual Pearson diffusions to exploit explicit solutions of the aforementioned equations. Moreover, we provide stochastic representation of such solutions in terms of time-changed Pearson diffusions. Finally, we exploit some further properties of these processes, such as limit distributions and long/short-range dependence.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Publisher:	Springer
ISSN:	0022-4715
Date of First Compliant Deposit:	10 June 2021
Date of Acceptance:	26 May 2021
Last Modified:	03 May 2023 18:40
URI:	https://orca.cardiff.ac.uk/id/eprint/141840

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