Strict continuity of the transition semigroup for the solution of a well-posed martingale problem
Probability
2020-10-01 v2 Functional Analysis
Abstract
In this note we connect the notion of solutions of a martingale problem to the notion of a strongly continuous and locally equi-continuous semigroup on the space of bounded continuous functions equipped with the strict topology. This extends the classical connection of semigroups to Markov processes that was used successfully in the context of compact spaces to the context of Polish spaces. In addition, we consider the context of locally compact spaces and show how the transition semigroup on the space of functions vanishing at infinity can be extended to the space of bounded continuous functions.
Keywords
Cite
@article{arxiv.1909.05113,
title = {Strict continuity of the transition semigroup for the solution of a well-posed martingale problem},
author = {Richard C. Kraaij},
journal= {arXiv preprint arXiv:1909.05113},
year = {2020}
}
Comments
arXiv admin note: text overlap with arXiv:1804.10222, arXiv:1404.2035