Summary
We consider Markov processes with a fixed transition functionp(r, x; t, B) and with random birth times. We show that a process\((\tilde X_t ,\tilde P)\) can be obtained from (X t ,P) by birth delay if and only if\(\tilde P\left\{ {\tilde X_t \in B} \right\} \leqq P\left\{ {X_t \in B} \right\}\) for allt andB. As an application, we give a new version and a new proof of the results of Rost [R] and Fitzsimmons [F2] on stopping distributions of Markov processes. The key Lemma 1.1 replaces the “filling scheme” used by the previous authors.
Birth delay was considered from a different prospective in [F1].
References
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Partially supported by the National Science Foundation Grant DMS-8802667
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Dynkin, E.B. Birth delay of a Markov process and the stopping distributions for regular processes. Probab. Th. Rel. Fields 94, 399–411 (1993). https://doi.org/10.1007/BF01199250
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DOI: https://doi.org/10.1007/BF01199250
Mathematics subject classification (1980)
- 60J25
- 60G40