The Annals of Probability

Applications of Raw Time-Changes to Markov Processes

Joseph Glover

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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 $\mathscr{F}_{T(t)} = \mathscr{F}_{T(t+)}$.

Article information

Source
Ann. Probab., Volume 9, Number 6 (1981), 1019-1029.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176994272

Digital Object Identifier
doi:10.1214/aop/1176994272

Mathematical Reviews number (MathSciNet)
MR632974

Zentralblatt MATH identifier
0473.60065

JSTOR
links.jstor.org

Subjects
Primary: 60J25: Continuous-time Markov processes on general state spaces
Secondary: 60G17: Sample path properties

Keywords
Markov process raw time-change continuous additive functional excursion terminal time

Citation

Glover, Joseph. Applications of Raw Time-Changes to Markov Processes. Ann. Probab. 9 (1981), no. 6, 1019--1029. doi:10.1214/aop/1176994272. https://projecteuclid.org/euclid.aop/1176994272


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