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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Kurt Helmes & Stefan Röhl & Richard H. Stockbridge, 2001. "Computing Moments of the Exit Time Distribution for Markov Processes by Linear Programming," Operations Research, INFORMS, vol. 49(4), pages 516-530, August.
    • Handle: RePEc:inm:oropre:v:49:y:2001:i:4:p:516-530
    DOI: 10.1287/opre.49.4.516.11221
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    References listed on IDEAS

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    1. Baxter,Martin & Rennie,Andrew, 1996. "Financial Calculus," Cambridge Books, Cambridge University Press, number 9780521552899, October.
    2. Dawson, Donald A., 1980. "Qualitative behavior of geostochastic systems," Stochastic Processes and their Applications, Elsevier, vol. 10(1), pages 1-31, June.
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    Cited by:

    1. Kurt Helmes & Stefan Röhl, 2008. "A Geometrical Characterization of Multidimensional Hausdorff Polytopes with Applications to Exit Time Problems," Mathematics of Operations Research, INFORMS, vol. 33(2), pages 315-326, May.

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