The Skorokhod problem with two nonlinear constraints (2306.16711v1)

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.