Ergodic properties of sum- and max-stable stationary random fields via null and positive group actions

DOI10.1214/11-AOP732zbMath1273.60062arXiv0911.0610MaRDI QIDQ1942115

Yizao Wang, Parthanil Roy, Stilian A. Stoev

Publication date: 15 March 2013

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

Full work available at URL: https://arxiv.org/abs/0911.0610

zbMATH Keywords

stableergodicityrandom fieldergodic theorymax-stablenonsingular group actionnull actionpositive action

Mathematics Subject Classification ID

Random fields (60G60) Stationary stochastic processes (60G10) Dynamical systems and their relations with probability theory and stochastic processes (37A50) Stable stochastic processes (60G52) Nonsingular (and infinite-measure preserving) transformations (37A40)

Related Items (17)

Ergodic decompositions of stationary max-stable processes in terms of their spectral functions ⋮ The tail process and tail measure of continuous time regularly varying stochastic processes ⋮ The realization problem for tail correlation functions ⋮ Tail measures and regular variation ⋮ On the continuity of Pickands constants ⋮ Representations of \(\max\)-stable processes via exponential tilting ⋮ Symmetric stable processes on amenable groups ⋮ A functional non-central limit theorem for multiple-stable processes with long-range dependence ⋮ Maxima of stable random fields, nonsingular actions and finitely generated abelian groups: a survey ⋮ On the association of sum- and max-stable processes ⋮ Maximal moments and uniform modulus of continuity for stable random fields ⋮ Stable random fields indexed by finitely generated free groups ⋮ Power variations for fractional type infinitely divisible random fields ⋮ Approximation of supremum of max-stable stationary processes \& Pickands constants ⋮ Decomposability for stable processes ⋮ Mixing properties of multivariate infinitely divisible random fields ⋮ Tail correlation functions of max-stable processes

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