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.

Non-local Solvable Birth–Death Processes / Ascione, G.; Leonenko, N.; Pirozzi, E.. - In: JOURNAL OF THEORETICAL PROBABILITY. - ISSN 0894-9840. - (2021). [10.1007/s10959-021-01087-4]

Non-local Solvable Birth–Death Processes

Ascione G.;Pirozzi E.
2021

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.
2021
Non-local Solvable Birth–Death Processes / Ascione, G.; Leonenko, N.; Pirozzi, E.. - In: JOURNAL OF THEORETICAL PROBABILITY. - ISSN 0894-9840. - (2021). [10.1007/s10959-021-01087-4]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11588/868566
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