Some sojourn time problems for 2-dimensional Gaussian processes

DOI10.1016/0047-259X(86)90058-8zbMath0593.60046MaRDI QIDQ1076416

Makoto Maejima

Publication date: 1986

Published in: Journal of Multivariate Analysis (Search for Journal in Brave)

zbMATH Keywords

stationary Gaussian processRosenblatt processoccupation time measure

Mathematics Subject Classification ID

Gaussian processes (60G15) Stationary stochastic processes (60G10) Convergence of probability measures (60B10)

Related Items

Sojourn measures of Student and Fisher-Snedecor random fields ⋮ Limiting theorems for sojourn measures in domains of vector-valued Gaussian random fields ⋮ Limit theorems for sojourn measures in domains of vector-valued Gaussian random fields

Cites Work

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• High level sojourns for strongly dependent Gaussian processes
• Some sojourn time problems for strongly dependent Gaussian processes
• Some limit theorems for sojourn times of strongly dependent Gaussian processes
• Weak convergence to fractional brownian motion and to the rosenblatt process
• Law of the iterated logarithm for sums of non-linear functions of Gaussian variables that exhibit a long range dependence
• Convergence of integrated processes of arbitrary Hermite rank
• Non-central limit theorems for non-linear functional of Gaussian fields