Veraverbeke's theorem at large: on the maximum of some processes with negative drift and heavy tail innovations

DOI10.1007/S10687-010-0103-9zbMath1226.60064arXiv0802.3638OpenAlexW2018140037MaRDI QIDQ650749

Philippe Barbe, William P. McCormick

Publication date: 27 November 2011

Published in: Extremes (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0802.3638

zbMATH Keywords

long range dependenceheavy tailboundary crossing probabilitymaximum of random walknonlinear renewal theoryfractional ARIMA process

Mathematics Subject Classification ID

Time series, auto-correlation, regression, etc. in statistics (GARCH) (62M10) Applications of statistics to actuarial sciences and financial mathematics (62P05) Fractional processes, including fractional Brownian motion (60G22) Extreme value theory; extremal stochastic processes (60G70) Sums of independent random variables; random walks (60G50) Large deviations (60F10) Applications of queueing theory (congestion, allocation, storage, traffic, etc.) (60K30)

Related Items (3)

Invariance principles for some FARIMA and nonstationary linear processes in the domain of a stable distribution ⋮ An extension of a logarithmic form of Cramér's ruin theorem to some FARIMA and related processes ⋮ Tauberian theorems for matrix regular variation

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• A note on Veraverbeke's theorem
• Estimates for the probability of ruin with special emphasis on the possibility of large claims
• Asymptotic behaviour of Wiener-Hopf factors of a random walk
• Large deviations results for subexponential tails, with applications to insurance risk
• Large deviations probabilities for random walks in the absence of finite expectations of jumps
• The supremum of a negative drift random walk with dependent heavy-tailed steps.
• Varieties of long memory models
• On distribution tail of the maximum of a random walk
• Large deviations and ruin probabilities for solutions to stochastic recurrence equations with heavy-tailed innovations
• On the tails of waiting-time distributions
• Precise large deviations for sums of random variables with consistently varying tails
• Convergence of weighted averages of independent random variables
• Integral Limit Theorems Taking Large Deviations into Account when Cramér’s Condition Does Not Hold. I
• Weak convergence of probability measures and random functions in the function space D[0,∞)
• Convergence of stochastic processes
• A Darboux-type theorem for slowly varying functions

This page was built for publication: Veraverbeke's theorem at large: on the maximum of some processes with negative drift and heavy tail innovations