Maxima of long memory stationary symmetric \(\alpha\)-stable processes, and self-similar processes with stationary max-increments

DOI10.3150/14-BEJ614zbMath1325.60040arXiv1307.2356MaRDI QIDQ2515510

Takashi Owada, Gennady Samorodnitsky

Publication date: 5 August 2015

Published in: Bernoulli (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1307.2356

zbMATH Keywords

functional limit theoremextreme value theoryself-similar processconservative flowpointwise dual ergodicitypartial maxima processsample maximastationary \(\alpha\)-stable process

Mathematics Subject Classification ID

Stationary stochastic processes (60G10) Extreme value theory; extremal stochastic processes (60G70) Self-similar stochastic processes (60G18) Stable stochastic processes (60G52) Functional limit theorems; invariance principles (60F17) Rate of growth of functions, orders of infinity, slowly varying functions (26A12)

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The tail process and tail measure of continuous time regularly varying stochastic processes ⋮ Limit theorems for conservative flows on multiple stochastic integrals ⋮ Extremes of Lévy-driven spatial random fields with regularly varying Lévy measure ⋮ A functional non-central limit theorem for multiple-stable processes with long-range dependence ⋮ Extreme value theory for long-range-dependent stable random fields ⋮ Long range dependence of heavy-tailed random functions ⋮ Maxima of stable random fields, nonsingular actions and finitely generated abelian groups: a survey ⋮ A family of random sup-measures with long-range dependence ⋮ Time-changed extremal process as a random sup measure ⋮ Stable random fields indexed by finitely generated free groups ⋮ Limit theorems for long-memory flows on Wiener chaos ⋮ Extremal theory for long range dependent infinitely divisible processes

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