On A Family of Isospectral Pure-Birth Processes

Laurent Miclo () and Chi Zhang
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Laurent Miclo: TSE-R - Toulouse School of Economics - UT Capitole - Université Toulouse Capitole - UT - Université de Toulouse - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, IMT - Institut de Mathématiques de Toulouse UMR5219 - UT Capitole - Université Toulouse Capitole - UT - Université de Toulouse - INSA Toulouse - Institut National des Sciences Appliquées - Toulouse - INSA - Institut National des Sciences Appliquées - UT - Université de Toulouse - UT2J - Université Toulouse - Jean Jaurès - UT - Université de Toulouse - UT3 - Université Toulouse III - Paul Sabatier - UT - Université de Toulouse - CNRS - Centre National de la Recherche Scientifique, CNRS - Centre National de la Recherche Scientifique, UT Capitole - Université Toulouse Capitole - UT - Université de Toulouse
Chi Zhang: OUC - Ocean University of China

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Abstract: It is shown that every spectrum of a finite irreducible Markov generator whose eigen-values are real and of geometric multiplicity 1 can be obtained as the spectrum of an irreducible pure-birth Markov process with jumps from the right-most boundary to all the other points. A whole isospectral family of such processes is exhibited and their mixing rates are compared.

Keywords: Pure-birth processes; Spectra of Markov processes; Mixing rates; Intertwining relations (search for similar items in EconPapers)
Date: 2021
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Published in ALEA : Latin American Journal of Probability and Mathematical Statistics, 2021, 18 (2), pp.1759-1771. ⟨10.30757/ALEA.v18-65⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-03605586

DOI: 10.30757/ALEA.v18-65

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