Summary
This paper studies processes constructed by birthing the trajectories of a given Markov process along time according to random probabilities. Getoor has considered the case where the random probabilities are determined by comultiplicative functionals and proved for right processes that the post-birth process has the Markov property. Here randomizations of comultiplicative functionals are described which give rise to conditionally Markov processes. The main argument is developed for general Markov processes and the transition probabilities of the new process, including those from the pre-birth state, are explicited.
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Sant'Anna, A.P. Birthing Markov processes at random rates. Z. Wahrscheinlichkeitstheorie verw Gebiete 44, 145–154 (1978). https://doi.org/10.1007/BF00533051
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DOI: https://doi.org/10.1007/BF00533051