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Non-local solvable birth-death processes

Ascione, Giacomo, Leonenko, Nikolai ORCID: 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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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

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