The Riesz representation theorem and weak${}^*$ compactness of semimartingales
Probability
2020-04-21 v9
Abstract
We show that the sequential closure of a family of probability measures on the canonical space of c{\`a}dl{\`a}g paths satisfying Stricker's uniform tightness condition is a weak compact set of semimartingale measures in the pairing of the Riesz representation theorem under topological assumptions on the path space. Similar results are obtained for quasi- and supermartingales under analogous conditions. In particular, we give a full characterization of the strongest topology on the Skorokhod space for which these results are true.
Keywords
Cite
@article{arxiv.1707.09382,
title = {The Riesz representation theorem and weak${}^*$ compactness of semimartingales},
author = {Matti Kiiski},
journal= {arXiv preprint arXiv:1707.09382},
year = {2020}
}
Comments
V1-V6 differ substantially from v7-v8 in exposition v9 adds lemma 3.5, example 3.9, remark 5.6, proposition 5.7 (i) and some other minor remarks