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Comparison of Markov processes via infinitesimal generators

Author

Listed:
  • Rüschendorf Ludger
  • Wolf Viktor

    (University of Freiburg, Mathematische Stochastik, Freiburg, Deutschland)

Abstract

We derive comparison results for Markov processes with respect to stochastic orderings induced by function classes. Our main result states that stochastic monotonicity of one process and comparability of the infinitesimal generators implies ordering of the processes. Unlike in previous work no boundedness assumptions on the function classes are needed anymore. We also present an integral version of the comparison result which does not need the local comparability assumption of the generators. The method of proof is also used to derive comparison results for time-discrete Markov processes.

Suggested Citation

  • Rüschendorf Ludger & Wolf Viktor, 2011. "Comparison of Markov processes via infinitesimal generators," Statistics & Risk Modeling, De Gruyter, vol. 28(2), pages 151-168, May.
    • Handle: RePEc:bpj:strimo:v:28:y:2011:i:2:p:151-168:n:4
    DOI: 10.1524/stnd.2011.1068
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    References listed on IDEAS

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    1. Greven, A. & Klenke, A. & Wakolbinger, A., 2002. "Interacting diffusions in a random medium: comparison and longtime behavior," Stochastic Processes and their Applications, Elsevier, vol. 98(1), pages 23-41, March.
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