Summary
Let X be a Markov process and M a homogeneous random set. For t≧0, we set G t=Sup{s≦t: s∈M}. The stochastic dependence between the past and the future of G Tis investigated for certain stopping times T. This gives some insight to recent results of Getoor concerning the excursion straddling t and the first excursion exceeding a in length.
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Getoor, R.K.: Excursions of a Markov process. [To appear in Ann. Probability]
Getoor, R.K., Sharpe, M.J.: Last exit decompositions and distributions. Indiana Univ. Math. J., 23, 377–404 (1973)
Maisonneuve, B.: Exit systems. Ann. Probability, 3, 309–411 (1975)
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This research was supported in part by NSF grant MCS76-8023
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Maisonneuve, B. On the structure of certain excursions of a Markov process. Z. Wahrscheinlichkeitstheorie verw Gebiete 47, 61–67 (1979). https://doi.org/10.1007/BF00533251
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DOI: https://doi.org/10.1007/BF00533251