Asymptotics for the moments of the overshoot and undershoot of a random walk

DOI10.1239/aap/1246886620zbMath1169.60321OpenAlexW2088584659MaRDI QIDQ5320661

Zhaolei Cui, Kai Yong Wang, Yue-bao Wang

Publication date: 22 July 2009

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

Full work available at URL: https://doi.org/10.1239/aap/1246886620

zbMATH Keywords

momentrenewal equationovershootundershootfirst ascending ladder heightlocal and nonlocal asymptotics

Mathematics Subject Classification ID

Applications of renewal theory (reliability, demand theory, etc.) (60K10) Applications of queueing theory (congestion, allocation, storage, traffic, etc.) (60K30) Renewal theory (60K05)

Related Items (16)

Random walks with non-convolution equivalent increments and their applications ⋮ Approximation formulas for the moments of the boundary functional of a Gaussian random walk with positive drift by using Siegmund's formula ⋮ Some discussions on the local distribution classes ⋮ Estimates for the overshoot of a random walk with negative drift and non-convolution equivalent increments ⋮ On asymptotic equivalence among the solutions of some defective renewal equations ⋮ The local asymptotic estimation for the supremum of a random walk with generalized strong subexponential summands ⋮ Local asymptotics of a Markov modulated random walk with heavy-tailed increments ⋮ Asymptotics for the solutions to defective renewal equations ⋮ The Uniform Asymptotics of the Overshoot of a Random Walk with Light-Tailed Increments ⋮ Tail behavior of supremum of a random walk when Cramér's condition fails ⋮ The closure of the convolution equivalent distribution class under convolution roots with applications to random sums ⋮ The Uniform Local Asymptotics of the Overshoot of a Random Walk with Heavy-Tailed Increments ⋮ On the almost decrease of a subexponential density ⋮ Note on the bi-risk discrete time risk model with income rate two ⋮ On a Sparre Andersen risk model perturbed by a spectrally negative Lévy process ⋮ Asymptotic formulas for the left truncated moments of sums with consistently varying distributed increments

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