Stochastic differential equations with respect to optional semimartingales and two reflecting regulated barriers
Probability
2022-02-28 v1
Abstract
In this work, we introduce a new Skorokhod problem with two reflecting barriers when the trajectories of the driven process and the barriers are right and left limited. We show that this problem has an explicit unique solution in a deterministic case. Then, we apply our result to study the existence and uniqueness of solutions of reflected stochastic differential equations with respect to optional semimartingales. The study is carried out on a probability space that does not necessarily satisfy the usual conditions.
Keywords
Cite
@article{arxiv.2202.12862,
title = {Stochastic differential equations with respect to optional semimartingales and two reflecting regulated barriers},
author = {Astrid Hilbert and Imane Jarni and Youssef Ouknine},
journal= {arXiv preprint arXiv:2202.12862},
year = {2022}
}