Non-local Solvable Birth–Death Processes

Giacomo Ascione (), Nikolai Leonenko () and Enrica Pirozzi ()
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Giacomo Ascione: Università degli Studi di Napoli Federico II
Nikolai Leonenko: Cardiff University
Enrica Pirozzi: Università degli Studi di Napoli Federico II

Journal of Theoretical Probability, 2022, vol. 35, issue 2, 1284-1323

Abstract: 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.

Keywords: Subordinator; Bernstein function; Classical orthogonal polynomial of discrete variable; 60K15; 33C45; 60G22 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10959-021-01087-4

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