On the restriction of a right process outside a negligible set
Abstract
The objective of this paper is to examine the restriction of a right process on a Radon topological space, excluding a negligible set, and investigate whether the restricted object can induce a Markov process with desirable properties. We address this question in three aspects: the induced process necessitates only right continuity; it is a right process, and the semi-Dirichlet form of the induced process is quasi-regular. The main findings characterize the negligible set that meets the requirements within a universally measurable framework. These characterizations can be employed to generate instances of Markov processes that are non-right or (semi-)Dirichlet forms that are non-quasi-regular. Specifically, we will construct an example of a non-tight, strong Feller, symmetric right process on a non-Lusin Radon topological space, whose Dirichlet form is not quasi-regular.
Keywords
Cite
@article{arxiv.2306.08520,
title = {On the restriction of a right process outside a negligible set},
author = {Liping Li and Michael Röckner},
journal= {arXiv preprint arXiv:2306.08520},
year = {2023}
}