A compound Poisson limit for stationary sums, and sojourns of Gaussian processes

DOI10.1214/aop/1176994725zbMath0439.60019OpenAlexW2051808061MaRDI QIDQ1142483

Simeon M. Berman

Publication date: 1980

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

Full work available at URL: https://doi.org/10.1214/aop/1176994725

zbMATH Keywords

stationary Gaussian processasymptotic independencesojourn timemixing conditioncompound Poisson distributionsum of stationary random variables

Mathematics Subject Classification ID

Gaussian processes (60G15) Central limit and other weak theorems (60F05) Stationary stochastic processes (60G10)

Related Items (9)

Semicontinuous processes in multi-dimensional extreme value theory ⋮ A central limit theorem for extreme sojourns of diffusion processes ⋮ Spectral conditions for sojourn and extreme value limit theorems for Gaussian processes ⋮ High level sojourns for strongly dependent Gaussian processes ⋮ High level sojourns of a diffusion process on a long interval ⋮ Gaussian stochastic processes ⋮ Testing monotonicity of regression. ⋮ On the excursion random measure of stationary processes ⋮ Limiting distribution of sums of nonnegative stationary random variables

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