A representation theorem for set-valued submartingales
Probability
2024-01-08 v2
Abstract
The integral representation theorem for martingales has been widely used in probability theory. In this work, we propose and prove a general representation theorem for a class of set-valued submartingales. We also extend the stochastic integral representation for non-trivial initial set-valued martingales. Moreover, we show that this result covers the existing ones in the literature for both degenerated and non-degenerated set-valued martingales.
Cite
@article{arxiv.2312.04006,
title = {A representation theorem for set-valued submartingales},
author = {Luc Tri Tuyen and Vu Thai Luan},
journal= {arXiv preprint arXiv:2312.04006},
year = {2024}
}