Tail probabilities of subadditive functionals of Lévy processes.

DOI10.1214/aoap/1015961156zbMath1035.60045OpenAlexW1972210419MaRDI QIDQ1872382

Michael Braverman, Thomas Mikosch, Gennady Samorodnitsky

Publication date: 6 May 2003

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

Full work available at URL: https://doi.org/10.1214/aoap/1015961156

zbMATH Keywords

heavy tailsriskruin probabilitysupremumnegtive drift

Mathematics Subject Classification ID

Infinitely divisible distributions; stable distributions (60E07) Processes with independent increments; Lévy processes (60G51)

Related Items (13)

Ruin problem and how fast stochastic processes mix ⋮ Functional regular variation of Lévy-driven multivariate mixed moving average processes ⋮ Heavy-traffic approximations for fractionally integrated random walks in the domain of attraction of a non-Gaussian stable distribution ⋮ Applications of factorization embeddings for Lévy processes ⋮ On subexponential tails for the maxima of negatively driven compound renewal and Lévy processes ⋮ Tail probabilities of subadditive functionals on stable processes with continuous and discrete time ⋮ Extremal behavior of regularly varying stochastic processes ⋮ Tail asymptotics for exponential functionals of Lévy processes ⋮ The point process approach for fractionally differentiated random walks under heavy traffic ⋮ Lévy Processes with Two-Sided Reflection ⋮ On regular variation for infinitely divisible random vectors and additive processes ⋮ Heavy tails of a Lévy process and its maximum over a random time interval ⋮ The probability of exceeding a high boundary on a random time interval for a heavy-tailed random walk

Cites Work

• Distributions of subadditive functionals of sample paths of infinitely divisible processes
• Estimates for the probability of ruin with special emphasis on the possibility of large claims
• Extremes of a certain class of Gaussian processes
• Ruin probability with claims modeled by a stationary ergodic stable process.
• An Extremal Problem in Probability Theory
• Subexponentiality and infinite divisibility
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