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Stable processes conditioned to avoid an interval

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  • Döring, Leif
  • Kyprianou, Andreas E.
  • Weissmann, Philip

Abstract

Conditioning Markov processes to avoid a domain is a classical problem that has been studied in many settings. Ingredients for standard arguments involve the leading order tail asymptotics of the distribution of the first hitting time of the domain of interest and its relation to an underlying harmonic function.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:130:y:2020:i:2:p:471-487
    DOI: 10.1016/j.spa.2019.01.004
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    References listed on IDEAS

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    1. Vysotsky, Vladislav, 2015. "Limit theorems for random walks that avoid bounded sets, with applications to the largest gap problem," Stochastic Processes and their Applications, Elsevier, vol. 125(5), pages 1886-1910.
    2. 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.
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