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

DOI10.1016/j.spa.2010.10.007zbMath1225.60076arXiv0712.2637OpenAlexW2034540049MaRDI QIDQ550133

Anatolii A. Puhalskii, Sergeĭ Georgievich Foss

Publication date: 8 July 2011

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0712.2637

zbMATH Keywords

borderline caseconvergence of conditional lawsrandom walk with negative driftspectrally positive Lévy process conditioned not to overshoottail asymptotics for the supremum

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Sums of independent random variables; random walks (60G50)

Related Items (4)

Approximation formulas for the moments of the boundary functional of a Gaussian random walk with positive drift by using Siegmund's formula ⋮ Boundary crossing problems for compound renewal processes ⋮ Upper Bounds for the Maximum of a Random Walk with Negative Drift ⋮ Customer sojourn time in \(GI/GI/1\) feedback queue in the presence of heavy tails

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The class of subexponential distributions
• Conditionings and path decompositions for Lévy processes
• A discrete renewal theorem with infinite mean
• Point processes, regular variation and weak convergence
• Conditioned limit theorems relating a random walk to its associate, with applications to risk reserve processes and the GI/G/1 queue
• Ruin probabilities expressed in terms of ladder height distributions
• Applied Probability and Queues
• Some asymptotic results for transient random walks
• Semi-stable Markov processes. I
• Conditioned stable Lévy processes and the Lamperti representation
• Strong Renewal Theorems with Infinite Mean
• Extreme Values in the GI/G/1 Queue
• The Distribution of the First Ladder Moment and Height and Fluctuation of a Random Walk
• On Probabilities of Large Deviations for Random Walks. II. Regular Exponentially Decaying Distributions

This page was built for publication: On the limit law of a random walk conditioned to reach a high level