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 $\mathscr{F}_{T(t)} = \mathscr{F}_{T(t+)}$.
Publié le : 1981-12-14
Classification:
Markov process,
raw time-change,
continuous additive functional,
excursion,
terminal time,
60J25,
60G17
@article{1176994272,
author = {Glover, Joseph},
title = {Applications of Raw Time-Changes to Markov Processes},
journal = {Ann. Probab.},
volume = {9},
number = {6},
year = {1981},
pages = { 1019-1029},
language = {en},
url = {http://dml.mathdoc.fr/item/1176994272}
}
Glover, Joseph. Applications of Raw Time-Changes to Markov Processes. Ann. Probab., Tome 9 (1981) no. 6, pp. 1019-1029. http://gdmltest.u-ga.fr/item/1176994272/