Cramér's estimate for a reflected Lévy process

DOI10.1214/105051605000000016zbMath1069.60045arXivmath/0505246OpenAlexW2018620178MaRDI QIDQ558683

Ross A. Maller, Ronald Arthur Doney

Publication date: 13 July 2005

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

Full work available at URL: https://arxiv.org/abs/math/0505246

zbMATH Keywords

Poisson limit theoremhigh excursionsmaximal segmental scoreMaximum of reflected process

Mathematics Subject Classification ID

Processes with independent increments; Lévy processes (60G51) Sample path properties (60G17)

Related Items

Curve crossing for random walks reflected at their maximum ⋮ Cramér's estimate for the reflected process revisited ⋮ The maximum of a Lévy process reflected at a general barrier ⋮ Tail asymptotics for exponential functionals of Lévy processes: the convolution equivalent case ⋮ A note on first passage probabilities of a L\'evy process reflected at a general barrier ⋮ Scan statistics of Lévy noises and marked empirical processes ⋮ General tax structures for a Lévy insurance risk process under the Cramér condition ⋮ Renewal theorems and stability for the reflected process ⋮ A lifetime of excursions through random walks and Lévy processes ⋮ Buffer-overflows: joint limit laws of undershoots and overshoots of reflected processes

Cites Work

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• Cramér's estimate for Lévy processes
• Conditioned limit theorems relating a random walk to its associate, with applications to risk reserve processes and the GI/G/1 queue
• Limit distributions of maximal segmental score among Markov-dependent partial sums
• The Strong Law of Large Numbers When the Mean is Undefined
• Extreme Values in the GI/G/1 Queue