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

Sergey G. Foss and Anatolii A. Puhalskii

Stochastic Processes and their Applications, 2011, vol. 121, issue 2, 288-313

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.

Keywords: Random; walk; with; negative; drift; Tail; asymptotics; for; the; supremum; Borderline; case; Convergence; of; conditional; laws; Spectrally; positive; Lévy; process; conditioned; not; to; overshoot (search for similar items in EconPapers)
Date: 2011
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