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

Kurt Helmes (), Stefan Röhl () and Richard H. Stockbridge ()
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Kurt Helmes: Institute of Operations Research, Humboldt University of Berlin, Berlin, Germany
Stefan Röhl: Konrad-Zuse-Zentrum für Informationstechnik Berlin, Berlin, Germany
Richard H. Stockbridge: Department of Statistics, University of Kentucky, Lexington, Kentucky

Operations Research, 2001, vol. 49, issue 4, 516-530

Abstract: 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.

Keywords: Application of linear programming; 60H35: Computation method for Markov processes; 60J25: Exit times of Markov processes (search for similar items in EconPapers)
Date: 2001
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