Journal of Probability and Statistics
Volume 2010 (2010), Article ID 846320, 18 pages
Research Article

An Explicit Representation of the Extended Skorokhod Map with Two Time-Dependent Boundaries

Department of Mathematics, Computer Science and Physics, Fairleigh Dickinson University, 285 Madison Ave, M-AB2-02, Madison, NJ 07940, USA

Received 28 December 2009; Accepted 27 April 2010

Academic Editor: A. Thavaneswaran

Copyright © 2010 Marek Slaby. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We consider the extended Skorokhod problem for real-valued càdlàg functions with the constraining interval [α,β], where α and β 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, J1 and M1, 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.