Asymptotics for the First Passage Times of Lévy Processes and Random Walks

DOI10.1239/jap/1363784425zbMath1264.60031arXiv0712.0728OpenAlexW2149124885MaRDI QIDQ4918563

Denis Denisov, Vsevolod Shneer

Publication date: 25 April 2013

Published in: Journal of Applied Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0712.0728

zbMATH Keywords

large deviationrandom walkfirst passage timeLévy processbusy periodsingle-server queuesubexponential distribution

Mathematics Subject Classification ID

Processes with independent increments; Lévy processes (60G51) Sums of independent random variables; random walks (60G50) Queueing theory (aspects of probability theory) (60K25)

Related Items (8)

The first passage time problem over a moving boundary for asymptotically stable Lévy processes ⋮ Asymptotics for exponential functionals of random walks ⋮ The boundary of random planar maps via looptrees ⋮ Asymptotic results for heavy-tailed Lévy processes and their exponential functionals ⋮ Global and local asymptotics for the busy period of an M/G/1 queue ⋮ First-passage time asymptotics over moving boundaries for random walk bridges ⋮ Tail asymptotics for the area under the excursion of a random walk with heavy-tailed increments ⋮ On busy periods of the critical GI/G/1 queue and BRAVO

Cites Work

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