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Non-local Solvable Birth–Death Processes

Author

Listed:
  • Giacomo Ascione

    (Università degli Studi di Napoli Federico II)

  • Nikolai Leonenko

    (Cardiff University)

  • Enrica Pirozzi

    (Università degli Studi di Napoli Federico II)

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.

Suggested Citation

  • Giacomo Ascione & Nikolai Leonenko & Enrica Pirozzi, 2022. "Non-local Solvable Birth–Death Processes," Journal of Theoretical Probability, Springer, vol. 35(2), pages 1284-1323, June.
    • Handle: RePEc:spr:jotpro:v:35:y:2022:i:2:d:10.1007_s10959-021-01087-4
    DOI: 10.1007/s10959-021-01087-4
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    References listed on IDEAS

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