Asymptotic Probabilities of an Exceedance Over Renewal Thresholds with an Application to Risk Theory

DOI10.1239/jap/1110381377zbMath1080.60054OpenAlexW1980476630MaRDI QIDQ5312847

Christian Y. Robert

Publication date: 25 August 2005

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

Full work available at URL: https://doi.org/10.1239/jap/1110381377

zbMATH Keywords

stopping timeheavy-tailed distributionregenerative processruin probabilityrenewal processmaximum of a random walk

Mathematics Subject Classification ID

Extreme value theory; extremal stochastic processes (60G70) Sums of independent random variables; random walks (60G50) Stopping times; optimal stopping problems; gambling theory (60G40) Applications of queueing theory (congestion, allocation, storage, traffic, etc.) (60K30)

Related Items

On the Maximum Exceedance of a Sequence of Random Variables Over a Renewal Threshold

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Estimates for the probability of ruin with special emphasis on the possibility of large claims
• Converse results for existence of moments and uniform integrability for stopped random walks
• Asymptotic behaviour of Wiener-Hopf factors of a random walk
• Subexponential asymptotics for stochastic processes: Extremal behavior, stationary distributions and first passage probabilities
• On the moments and limit distributions of some first passage times
• The maximum on a random time interval of a random walk with long-tailed increments and negative drift.
• On distribution tail of the maximum of a random walk
• Subexponential distributions and integrated tails
• Moments of Randomly Stopped Sums