Penalization for Birth and Death Processes

Pierre Debs () and Mihai Gradinaru ()
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Pierre Debs: Institut Élie Cartan Nancy
Mihai Gradinaru: Institut de Recherche Mathematique de Rennes

Journal of Theoretical Probability, 2008, vol. 21, issue 3, 745-771

Abstract: 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 (search for similar items in EconPapers)
Date: 2008
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DOI: 10.1007/s10959-007-0123-9

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