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Journal of Theoretical Probability

, Volume 21, Issue 3, pp 745–771 | Cite as

Penalization for Birth and Death Processes

  • Pierre Debs
  • Mihai GradinaruEmail author
Article

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.

Keywords

Birth and death Markov processes Penalization Sojourn time Dynkin’s formula Random walk Brownian motion with drift Bessel chain and process Change of probability 

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Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.Institut Élie Cartan NancyVandœuvre-lès-Nancy CedexFrance
  2. 2.Institut de Recherche Mathematique de RennesRennes CedexFrance

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