The Skorokhod problem with two nonlinear constraints
Abstract:
In this paper, we study the Skorokhod problem with two constraints,
where both constraints are nonlinear. We prove the existence and
uniqueness of a solution and also provide an explicit construction for
the solution. In addition, a number of properties of the solution are
investigated, including continuity under uniform and J1 metrics and a
comparison principle.
2010 AMS Mathematics Subject Classification: Primary 60G05; Secondary 60G17.
Keywords and phrases: Skorokhod problem, nonlinear reflecting boundaries,
double reflecting boundaries, comparison principle.