Multi-occupation field generates the Borel-sigma-field of loops
Probability
2013-12-17 v2
Abstract
In this article, we consider the space of c\`{a}dl\`{a}g loops on a Polish space . The loop space can be equipped with a ``Skorokhod'' metric. Moreover, it is Polish under this metric. Our main result is to prove that the Borel--field on the space of loops is generated by a class of loop functionals: the multi-occupation field. This result generalizes the result in the discrete case, see \cite{loop}.
Keywords
Cite
@article{arxiv.1309.1558,
title = {Multi-occupation field generates the Borel-sigma-field of loops},
author = {Yinshan Chang},
journal= {arXiv preprint arXiv:1309.1558},
year = {2013}
}