Time change is one of the most basic and very useful transformations for Markov processes. The time changed process can also be regarded as the trace of the original process on the support of the Revuz measure used in the time change. In this paper we give a complete characterization of time changed processes of an arbitrary symmetric Markov process, in terms of the Beurling–Deny decomposition of their associated Dirichlet forms and of Feller measures of the process. In particular, we determine the jumping and killing measure (or, equivalently, the Lévy system) for the time-changed process. We further discuss when the trace Dirichlet form for the time changed process can be characterized as the space of finite Douglas integrals defined by Feller measures. Finally, we give a probabilistic characterization of Feller measures in terms of the excursions of the base process.
Publié le : 2006-05-14
Classification:
Symmetric right process,
time change,
trace,
positive continuous additive functional,
Revuz measure,
Dirichlet form,
reflected Dirichlet space,
energy functional,
Feller measure,
supplementary Feller measure,
Douglas integral,
stochastic analysis,
martingale additive functional,
energy measure,
excursion,
60J45,
60J50,
31C25
@article{1151418493,
author = {Chen, Zhen-Qing and Fukushima, Masatoshi and Ying, Jiangang},
title = {Traces of symmetric Markov processes and their characterizations},
journal = {Ann. Probab.},
volume = {34},
number = {1},
year = {2006},
pages = { 1052-1102},
language = {en},
url = {http://dml.mathdoc.fr/item/1151418493}
}
Chen, Zhen-Qing; Fukushima, Masatoshi; Ying, Jiangang. Traces of symmetric Markov processes and their characterizations. Ann. Probab., Tome 34 (2006) no. 1, pp. 1052-1102. http://gdmltest.u-ga.fr/item/1151418493/