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