The Skorokhod problem with two nonlinear constraints

TL;DR

This paper investigates the Skorokhod problem with two nonlinear constraints, establishing existence, uniqueness, explicit solutions, and key properties such as continuity, comparison principle, and non-anticipation.

Contribution

It provides the first explicit construction and analysis of solutions to the Skorokhod problem with nonlinear constraints, expanding the theoretical framework.

Findings

Proved existence and uniqueness of solutions.

Derived explicit construction of solutions.

Analyzed properties like continuity and comparison principle.

Abstract

In this paper, we study the Skorokhod problem with two constraints, where the constraints are in a nonlinear fashion. We prove the existence and uniqueness of the solution and also provide the explicit construction for the solution. In addition, a number of properties of the solution, including continuity under uniform and J1 metrics, comparison principle and non-anticipatory property, are investigated.