A Unified Approach to the Heavy-Traffic Analysis of the Maximum of Random Walks

DOI10.1137/S0040585X97984796zbMath1229.60059OpenAlexW2004347303MaRDI QIDQ5198651

Vitali Wachtel, Vsevolod Shneer

Publication date: 9 August 2011

Published in: Theory of Probability & Its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/s0040585x97984796

zbMATH Keywords

stable lawrandom walkglobal maximumKolmogorov inequality generalization

Mathematics Subject Classification ID

Infinitely divisible distributions; stable distributions (60E07) Extreme value theory; extremal stochastic processes (60G70) Sums of independent random variables; random walks (60G50) Queueing theory (aspects of probability theory) (60K25) Stable stochastic processes (60G52) Functional limit theorems; invariance principles (60F17)

Related Items (10)

Persistence of heavy-tailed sample averages: principle of infinitely many big jumps ⋮ Sample path large deviations for Lévy processes and random walks with regularly varying increments ⋮ A tandem fluid network with Lévy input in heavy traffic ⋮ Limit theorems for discounted convergent perpetuities. II ⋮ Heavy-traffic approximations for fractionally integrated random walks in the domain of attraction of a non-Gaussian stable distribution ⋮ Convergence of the all-time supremum of a Lévy process in the heavy-traffic regime ⋮ Small drift limit theorems for random walks ⋮ Single-server queues under overdispersion in the heavy-traffic regime ⋮ Disorder and denaturation transition in the generalized Poland-Scheraga model ⋮ Heavy-traffic asymptotics for networks of parallel queues with Markov-modulated service speeds

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