On the excursion random measure of stationary processes

DOI10.1214/aop/1022855648zbMath0935.60013OpenAlexW2086850236MaRDI QIDQ1307503

M. Ross Leadbetter, Tailen Hsing

Publication date: 1 February 2000

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

Full work available at URL: https://doi.org/10.1214/aop/1022855648

zbMATH Keywords

weak convergenceinfinite divisibilityextremessojourns

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Stationary stochastic processes (60G10)

Related Items (6)

On some estimates based on sample behavior near high level excursions ⋮ The tail process and tail measure of continuous time regularly varying stochastic processes ⋮ On multiple-level excursions by stationary processes with deterministic peaks ⋮ A complete convergence theorem for stationary regularly varying multivariate time series ⋮ Sojourn times and the fragility index ⋮ Palm theory, random measures and Stein couplings

Cites Work

• Extremes and related properties of random sequences and processes
• Sojourns of stationary processes in rare sets
• On the exceedance point process for a stationary sequence
• On the characterization of certain point processes
• Extremal theory for stochastic processes
• A compound Poisson limit for stationary sums, and sojourns of Gaussian processes
• Sojourns and extremes of stationary processes
• Limit theorems for strongly mixing stationary random measures
• Extremes of moving averages of stable processes
• Stationary self-similar extremal processes
• On some estimates based on sample behavior near high level excursions
• On multiple-level excursions by stationary processes with deterministic peaks
• Extremes and local dependence in stationary sequences
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