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Penalization for birth and death processes. (English) Zbl 1149.60056
Summary: 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.
MSC:
60J80 Branching processes (Galton-Watson, birth-and-death, etc.)
60J25 Continuous-time Markov processes on general state spaces
60J55 Local time and additive functionals
60G44 Martingales with continuous parameter
60G46 Martingales and classical analysis
60J60 Diffusion processes
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