An explicit representation of the extended Skorokhod map with two time-dependent boundaries (Q609726)

Summary: We consider the extended Skorokhod problem for real-valued càdlàg functions with the constraining interval \([\alpha ,\beta ]\), where \(\alpha \) and \(\beta \) change in time as values of two càdlàg functions. We find an explicit form of the solution and discuss its continuity properties with respect to the uniform, \(J_{1}\) and \(M_{1}\), metrics on the space of càdlàg functions. We develop a useful technique of extending known results for the Skorokhod maps onto the larger class of extended Skorokhod maps.