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December, 1981 Applications of Raw Time-Changes to Markov Processes
Joseph Glover
Ann. Probab. 9(6): 1019-1029 (December, 1981). DOI: 10.1214/aop/1176994272

Abstract

The technique of raw time-change is applied to give another proof that the Knight-Pittenger procedure of deleting excursions of a strong Markov process from a set $A$ which meet a disjoint set $B$ yields a strong Markov process. A natural filtration is associated with the new process, and generalizations are given. Under natural hypotheses, the debuts of a class of nonadapted homogeneous sets are shown to be killing times of a strong Markov process. These are generalized (i.e. raw) terminal times. Let $A_t$ be an increasing nonadapted continuous process, and let $T_t$ be its right continuous inverse satisfying a hypothesis which ensures that the collection of $\sigma$-fields $\mathscr{F}_{T(t)}$ is increasing. The optional times of $\mathscr{F}_{T(t)}$ are characterized in terms of killing operators and the points of increase of $A$, and it is shown that $\mathscr{F}_{T(t)} = \mathscr{F}_{T(t+)}$.

Citation

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Joseph Glover. "Applications of Raw Time-Changes to Markov Processes." Ann. Probab. 9 (6) 1019 - 1029, December, 1981. https://doi.org/10.1214/aop/1176994272

Information

Published: December, 1981
First available in Project Euclid: 19 April 2007

zbMATH: 0473.60065
MathSciNet: MR632974
Digital Object Identifier: 10.1214/aop/1176994272

Subjects:
Primary: 60J25
Secondary: 60G17

Rights: Copyright © 1981 Institute of Mathematical Statistics

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Vol.9 • No. 6 • December, 1981
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