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Coterminal families and the strong Markov property


Authors: A. O. Pittenger and C. T. Shih
Journal: Trans. Amer. Math. Soc. 182 (1973), 1-42
MSC: Primary 60J40
DOI: https://doi.org/10.1090/S0002-9947-1973-0336827-2
MathSciNet review: 0336827
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Abstract: Let $ {E_\Delta }$ be a compact metric space and assume that a strong Markov process X is defined on $ {E_\Delta }$. Under the assumption that X has right continuous paths with left limits, it is shown that a version of the strong Markov property extends to coterminal families, a class of random times which can be visualized as last exit times before t from a fixed subset of $ {E_\Delta }$. Since the random times are not Markov times, the conditioning $ \sigma $-field and the new conditional probabilities must be defined. If X is also assumed to be nearly quasileft continuous, i.e. branching points are permitted, two different conditionings are possible--one on the ``past'' of the random time and one on the ``past plus present"--and two different conditional probabilities must be defined.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1973-0336827-2
Keywords: Markov process, strong Markov property, Hunt process, Standard process, last exit time, coterminal time
Article copyright: © Copyright 1973 American Mathematical Society

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