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On A Family of Isospectral Pure-Birth Processes

Author

Listed:
  • 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)

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.

Suggested Citation

  • Laurent Miclo & Chi Zhang, 2021. "On A Family of Isospectral Pure-Birth Processes," Post-Print hal-03605586, HAL.
    • Handle: RePEc:hal:journl:hal-03605586
    DOI: 10.30757/ALEA.v18-65
    as

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