On the Extension of the Class of Stable Distributions

DOI10.1137/1117081zbMath0279.60035OpenAlexW2094871289MaRDI QIDQ4765807

Victor M. Kruglov

Publication date: 1972

Published in: Theory of Probability & Its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/1117081

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Sums of independent random variables; random walks (60G50) Probability distributions: general theory (60E05)

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Asymptotic behavior of the generalized St. Petersburg sum conditioned on its maximum ⋮ Supplements to operator-stable and operator-semistable laws on Euclidean spaces ⋮ Merging of linear combinations to semistable laws ⋮ Functional law of the iterated logarithm for partial sum processes of non-negative valued iid random variables belonging to the domain of partial attraction of a semi-stable law ⋮ ON LÉVY STABLE AND SEMISTABLE DISTRIBUTIONS ⋮ Series representation for semistable laws and their domains of semistable attraction ⋮ An almost sure functional limit theorem for the domain of geometric partial attraction of semistable laws ⋮ Moments of measures attracted to operator semi-stable laws ⋮ Recurrence and transience of operator semi-stable processes ⋮ Multiparameter Shimizu equation ⋮ Characterization of multivariate distributions through a functional equation of their characteristic functions ⋮ Discrete semistable probability distributions ⋮ Semistable measures on a Hilbert space ⋮ Generalized semistable probability distributions in Hilbert space ⋮ Law of iterated logarithm for random subsequences ⋮ A note on asymptotics of linear combinations of IID random variables ⋮ On a functional equation generalizing the class of semistable distributions ⋮ Law of iterated logarithm and almost sure limit points for random sums ⋮ A characterization of gamma mixtures of stable laws motivated by limit theorems ⋮ A law of the iterated logarithm for semistable laws on vector spaces and homogeneous groups ⋮ Limit theorems for probability measures on simply connected nilpotent Lie groups ⋮ Merging asymptotic expansions for semistable random variables ⋮ Operator semistable probability measures on a Hilbert space ⋮ Limit theorems for wobbly interval intermittent maps ⋮ On Lévy-Fréchet processes and related self-similar and semi-self-similar ones

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