Non-local solvable birth-death processes

Ascione, Giacomo, Leonenko, Nikolai ORCID: https://orcid.org/0000-0003-1932-4091 and Pirozzi, Enrica 2022. Non-local solvable birth-death processes. Journal of Theoretical Probability 35 , pp. 1284-1323. 10.1007/s10959-021-01087-4

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Abstract

In this paper, we study strong solutions of some non-local difference–differential equations linked to a class of birth–death processes arising as discrete approximations of Pearson diffusions by means of a spectral decomposition in terms of orthogonal polynomials and eigenfunctions of some non-local derivatives. Moreover, we give a stochastic representation of such solutions in terms of time-changed birth–death processes and study their invariant and their limit distribution. Finally, we describe the correlation structure of the aforementioned time-changed birth–death processes.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Additional Information:	This article is licensed under a Creative Commons Attribution 4.0 International License
Publisher:	Springer Verlag (Germany)
ISSN:	0894-9840
Date of First Compliant Deposit:	25 March 2021
Date of Acceptance:	3 March 2021
Last Modified:	02 May 2023 13:17
URI:	https://orca.cardiff.ac.uk/id/eprint/140120

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