Symmetric stable processes on amenable groups

DOI10.4064/sm220924-19-2arXiv2205.04159MaRDI QIDQ6135685

Nachi Avraham-Re'em

Publication date: 25 August 2023

Published in: Studia Mathematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2205.04159

zbMATH Keywords

spectral representationstationary processamenable groupstable processnonsingular group action

Mathematics Subject Classification ID

Infinitely divisible distributions; stable distributions (60E07) Random fields (60G60) Stationary stochastic processes (60G10) Stable stochastic processes (60G52) Nonsingular (and infinite-measure preserving) transformations (37A40)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Maharam extension and stationary stable processes
• The equivalence of ergodicity and weak mixing for infinitely divisible processes
• Amenable semigroups
• Ergodic theorems. With a supplement by Antoine Brunel
• Ergodic properties of stationary stable processes
• On the spectral representation of symmetric stable processes
• A note on ergodic symmetric stable processes
• Stable mixed moving averages
• Some mixing conditions for stationary symmetric stable stochastic processes
• Classes of mixing stable processes
• Pointwise theorems for amenable groups.
• Bernoulli actions of type \(\mathrm{III}_{1}\) and \(L^2\)-cohomology
• Stable random fields indexed by finitely generated free groups
• Singular compactness and the Neveu decomposition
• Decomposition of stationary \(\alpha\)-stable random fields.
• On the structure of stationary stable processes
• Ergodic properties of sum- and max-stable stationary random fields via null and positive group actions
• On the \(K\) property for Maharam extensions of Bernoulli shifts and a question of Krengel
• The orbital equivalence of Bernoulli actions and their Sinai factors
• Ergodicity and type of nonsingular Bernoulli actions
• Ergodic properties of Poissonian ID processes
• Stationary symmetric \(\alpha\)-stable discrete parameter random fields
• Compact semitopological semigroups and weakly almost periodic functions
• Null flows, positive flows and the structure of stationary symmetric stable processes
• On equivalence of infinite product measures
• A contribution to the theory of divergent sequences
• Finite ergodic index and asymmetry for infinite measure preserving actions
• Stochastic Processes and Long Range Dependence
• On a type III₁Bernoulli shift
• On a Bernoulli shift with non-identical factor measures
• Directional recurrence and directional rigidity for infinite measure preserving actions of nilpotent lattices
• A large sample test for the length of memory of stationary symmetric stable random fields via nonsingular ℤ^d-actions
• The zero-type property and mixing of Bernoulli shifts
• Unitary Representations of Groups, Duals, and Characters
• K-property for Maharam extensions of non-singular Bernoulli and Markov shifts
• Folner's Conditions for Amenable Semi-Groups.
• On the Ergodic Mixing Theorem
• On a Concept of Summability in Amenable Groups.
• Some Structure Theorems for the Symmetric Stable Laws
• Invariant functions for amenable semigroups of positive contractions on $L^{1}$
• A generalization of a problem of Steinhaus
• A representation theorem for symmetric stable processes and stable measures on H
• Weakly Wandering Sets and Invariant Measures
• Ergodic Theory