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A duality relation for entrance and exit laws for Markov processes

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  • Cox, J. Theodore
  • Rösler, Uwe

Abstract

Markov processes Xt on (X, FX) and Yt on (Y, FY) are said to be dual with respect to the function f(x, y) if Exf(Xt, y) = Eyf(x, Yt for all x [epsilon] X, y [epsilon] Y, t [greater-or-equal, slanted] 0. It is shown that this duality reverses the role of entrance and exit laws for the processes, and that two previously published results of the authors are dual in precisely this sense. The duality relation for the function f(x, y) = 1{x

Suggested Citation

  • Cox, J. Theodore & Rösler, Uwe, 1984. "A duality relation for entrance and exit laws for Markov processes," Stochastic Processes and their Applications, Elsevier, vol. 16(2), pages 141-156, February.
    • Handle: RePEc:eee:spapps:v:16:y:1984:i:2:p:141-156
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    Cited by:

    1. Anja Sturm & Jan M. Swart, 2018. "Pathwise Duals of Monotone and Additive Markov Processes," Journal of Theoretical Probability, Springer, vol. 31(2), pages 932-983, June.
    2. Foucart, Clément & Möhle, Martin, 2022. "Asymptotic behaviour of ancestral lineages in subcritical continuous-state branching populations," Stochastic Processes and their Applications, Elsevier, vol. 150(C), pages 510-531.
    3. Foucart, Clément & Vidmar, Matija, 2024. "Continuous-state branching processes with collisions: First passage times and duality," Stochastic Processes and their Applications, Elsevier, vol. 167(C).
    4. Holger Dette & James Allen Fill & Jim Pitman & William J. Studden, 1997. "Wall and Siegmund Duality Relations for Birth and Death Chains with Reflecting Barrier," Journal of Theoretical Probability, Springer, vol. 10(2), pages 349-374, April.

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