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Penalization for Birth and Death Processes

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Abstract

In this paper we study a transient birth and death Markov process penalized by its sojourn time in 0. Under the new probability measure the original process behaves as a recurrent birth and death Markov process. We also show, in a particular case, that an initially recurrent birth and death process behaves as a transient birth and death process after penalization with the event that it can reach zero in infinite time. We illustrate some of our results with the Bessel random walk example.

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Authors and Affiliations

  1. Institut Élie Cartan Nancy, B.P. 239, 54506, Vandœuvre-lès-Nancy Cedex, France

    Pierre Debs

  2. Institut de Recherche Mathematique de Rennes, Campus de Beaulieu, 35042, Rennes Cedex, France

    Mihai Gradinaru

Authors
  1. Pierre Debs
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  2. Mihai Gradinaru
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Correspondence to Mihai Gradinaru.

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Debs, P., Gradinaru, M. Penalization for Birth and Death Processes. J Theor Probab 21, 745–771 (2008). https://doi.org/10.1007/s10959-007-0123-9

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  • DOI: https://doi.org/10.1007/s10959-007-0123-9

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