# On Skorokhod Problem with Two RCLL Reflecting Completely Separated Barriers

## TL;DR

This paper establishes existence and uniqueness results for the Skorokhod problem with separated RCLL barriers and applies these findings to reflected stochastic differential equations.

## Contribution

It provides new theoretical results on the Skorokhod problem with RCLL barriers and extends these to solutions of reflected SDEs.

## Key findings

- Existence and uniqueness of solutions for the Skorokhod problem with separated RCLL barriers.
- Application of Skorokhod problem results to reflected stochastic differential equations.
- Theoretical framework for RCLL barriers in stochastic reflection problems.

## Abstract

In this paper we deal with Skorokhod problem for right continuous left limited (rcll) barriers. We prove existence and uniqueness of the solution when the barriers are only supposed to be rcll and completely separated. Then, we apply our results to prove existence and uniqueness of the solution of a reflected stochastic differential equation (SDE).