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

We consider the extended skorokhod problem for real-valued cdlg functions with the constraining interval [α,β],where α and β change in time as values of two cdlg 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 cdlg functions. we develop a useful technique of extending known results for the skorokhod maps onto the larger class of extended skorokhod maps. © 2010 marek slaby.