When is the cluster set of S//n/\(a_ n\) empty?

DOI10.1214/aop/1176994412zbMath0459.60005OpenAlexW2012677450MaRDI QIDQ1152156

James Kuelbs

Publication date: 1981

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

Full work available at URL: https://doi.org/10.1214/aop/1176994412

zbMATH Keywords

law of the iterated logarithmcentral limit theoremreproducing kernel Hilbert spacecluster setBanach space valued random variablerates of escape

Mathematics Subject Classification ID

Probability measures on topological spaces (60B05) Convergence of probability measures (60B10) Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) (28C20) Probability theory on linear topological spaces (60B11) Limit theorems for vector-valued random variables (infinite-dimensional case) (60B12)

Related Items (11)

Cluster sets for a generalized law of the iterated logarithm in Banach spaces ⋮ Small deviations for admixture additive \& multiplicative processes ⋮ Cluster sets of self-normalized sums ⋮ The law of the iterated logarithm for subsequences and characterization of the cluster set of \(S_{n_ k}/(2n_ k\log \,\log \,n_ k)^{1/2}\) in Banach spaces ⋮ Lil behavior for weakly dependent random variables in Banach spaces ⋮ Cluster sets for partial sums and partial sum processes ⋮ A LIL for independent non-identically distributed random variables in Banach space and its applications ⋮ LIL behavior for B-valued strong mixing random variables ⋮ How often does a Harris recurrent Markov chain recur? ⋮ Angular asymptotics for random walks ⋮ Some results on two-sided LIL behavior

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