This Article Full Text (PDF) References Alert me when this article is cited Alert me if a correction is posted Services Email this article to a friend Similar articles in this journal Alert me to new issues of the journal Download to citation manager Citing Articles Citing Articles via Google Scholar Google Scholar Articles by Helmes, K. Articles by Stockbridge, R. H. Search for Related Content

Computing Moments of the Exit Time Distribution for Markov Processes by Linear Programming

Institute of Operations Research, Humboldt University of Berlin, Berlin, Germany
Konrad-Zuse-Zentrum für Informationstechnik Berlin, Berlin, Germany
Department of Statistics, University of Kentucky, Lexington, Kentucky
helmes{at}wiwi.hu-berlin.de
roehl{at}zib.de
stockb{at}ms.uky.edu

We provide a new approach to the numerical computation of moments of the exit time distribution of Markov processes. The method relies on a linear programming formulation of a process exiting from a bounded domain. The LP formulation characterizes the evolution of the process through the moments of the induced occupation measure and naturally provides upper and lower bounds for the exact values of the moments. The conditions the moments have to satisfy are derived directly from the generator of the Markov process and are not based on some approximation of the process. Excellent software is readily available because the computations involve finite dimensional linear programs.

Subject classifications: Application of linear programming; 60H35: Computation method for Markov processes; 60J25: Exit times of Markov processes.
History: Received October 1997; revision received February 1999; revision received January 2000; accepted April 2000.