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On the limit law of a random walk conditioned to reach a high level

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  • Foss, Sergey G.
  • Puhalskii, Anatolii A.

Abstract

We consider a random walk with a negative drift and with a jump distribution which under Cramér's change of measure belongs to the domain of attraction of a spectrally positive stable law. If conditioned to reach a high level and suitably scaled, this random walk converges in law to a nondecreasing Markov process which can be interpreted as a spectrally positive Lévy process conditioned not to overshoot level 1.

Suggested Citation

  • Foss, Sergey G. & Puhalskii, Anatolii A., 2011. "On the limit law of a random walk conditioned to reach a high level," Stochastic Processes and their Applications, Elsevier, vol. 121(2), pages 288-313, February.
    • Handle: RePEc:eee:spapps:v:121:y:2011:i:2:p:288-313
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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.
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