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Conditioning subordinators embedded in Markov processes

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  • Kyprianou, Andreas E.
  • Rivero, Victor
  • Şengül, Batı

Abstract

The running infimum of a Lévy process relative to its point of issue is known to have the same range that of the negative of a certain subordinator. Conditioning a Lévy process issued from a strictly positive value to stay positive may therefore be seen as implicitly conditioning its descending ladder height subordinator to remain in a strip. Motivated by this observation, we consider the general problem of conditioning a subordinator to remain in a strip. Thereafter we consider more general contexts in which subordinators embedded in the path decompositions of Markov processes are conditioned to remain in a strip.

Suggested Citation

  • Kyprianou, Andreas E. & Rivero, Victor & Şengül, Batı, 2017. "Conditioning subordinators embedded in Markov processes," Stochastic Processes and their Applications, Elsevier, vol. 127(4), pages 1234-1254.
    • Handle: RePEc:eee:spapps:v:127:y:2017:i:4:p:1234-1254
    DOI: 10.1016/j.spa.2016.07.013
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    References listed on IDEAS

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    1. Chaumont, L., 1996. "Conditionings and path decompositions for Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 64(1), pages 39-54, November.
    2. Haas, Bénédicte & Rivero, Víctor, 2012. "Quasi-stationary distributions and Yaglom limits of self-similar Markov processes," Stochastic Processes and their Applications, Elsevier, vol. 122(12), pages 4054-4095.
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    Cited by:

    1. Kyprianou, Andreas E. & Rivero, Víctor M. & Satitkanitkul, Weerapat, 2019. "Conditioned real self-similar Markov processes," Stochastic Processes and their Applications, Elsevier, vol. 129(3), pages 954-977.
    2. Döring, Leif & Kyprianou, Andreas E. & Weissmann, Philip, 2020. "Stable processes conditioned to avoid an interval," Stochastic Processes and their Applications, Elsevier, vol. 130(2), pages 471-487.
    3. Kyprianou, Andreas E. & Palau, Sandra & Saizmaa, Tsogzolmaa, 2021. "Attraction to and repulsion from a subset of the unit sphere for isotropic stable Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 137(C), pages 272-293.

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