Local asymptotics of the cycle maximum of a heavy-tailed random walk

DOI10.1239/aap/1175266476zbMath1114.60038OpenAlexW1995154657MaRDI QIDQ3435397

Denis Denisov, Vsevolod Shneer

Publication date: 26 April 2007

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

Full work available at URL: https://doi.org/10.1239/aap/1175266476

zbMATH Keywords

stopping timeheavy-tailed distributionrandom walksubexponential distributionbusy cycle

Mathematics Subject Classification ID

Extreme value theory; extremal stochastic processes (60G70) Sums of independent random variables; random walks (60G50)

Related Items

State-independent Importance Sampling for Random Walks with Regularly Varying Increments ⋮ Asymptotics for the moments of the overshoot and undershoot of a random walk ⋮ Random walks with non-convolution equivalent increments and their applications ⋮ Some discussions on the local distribution classes ⋮ Local asymptotics of a Markov modulated random walk with heavy-tailed increments ⋮ Large deviations for random walks under subexponentiality: The big-jump domain ⋮ The closure of the convolution equivalent distribution class under convolution roots with applications to random sums ⋮ Maximum on a random time interval of a random walk with infinite mean ⋮ The Uniform Local Asymptotics of the Overshoot of a Random Walk with Heavy-Tailed Increments ⋮ On the almost decrease of a subexponential density

Cites Work

• Tail asymptotics for the supremum of a random walk when the mean is not finite
• On the asymptotic behavior of the distributions of first-passage times. I.
• Subexponential asymptotics for stochastic processes: Extremal behavior, stationary distributions and first passage probabilities
• Patterns of buffer overflow in a class of queues with long memory in the input stream
• Asymptotics for sums of random variables with local subexponential behaviour
• A local limit theorem for random walk maxima with heavy tails
• The maximum on a random time interval of a random walk with long-tailed increments and negative drift.
• The probability of exceeding a high boundary on a random time interval for a heavy-tailed random walk
• Tail Asymptotics for the Busy Period in the GI/G/1 Queue
• Subexponential distributions and integrated tails
• Subexponential Distributions - Large Deviations with Applications to Insurance and Queueing Models
• Applied Probability and Queues
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item