Stable Measures and Central Limit Theorems in Spaces of Stable Type

DOI10.2307/1998684zbMath0449.60003OpenAlexW4233880360MaRDI QIDQ3896287

Wojbor A. Woyczyński, Michael B. Marcus

Publication date: 1979

Full work available at URL: https://doi.org/10.2307/1998684

zbMATH Keywords

central limit theoremweak law of large numbersdomains of attractionrandom integralquasi-normed spacestable measuresspace of stable type p

Mathematics Subject Classification ID

Infinitely divisible distributions; stable distributions (60E07) Central limit and other weak theorems (60F05) Sums of independent random variables; random walks (60G50) Geometry and structure of normed linear spaces (46B20) Convergence of probability measures (60B10) Probability theory on linear topological spaces (60B11) Limit theorems for vector-valued random variables (infinite-dimensional case) (60B12)

Related Items (max. 100)

Rate of convergence in the weak law of large numbers in a Banach space ⋮ On stochastic integral representation of stable processes with sample paths in Banach spaces ⋮ Stochastic multiplicative measures, generalized Markov semigroups, and group-valued stochastic processes and fields ⋮ Continuity of symmetric stable processes ⋮ A probability inequality for sums of independent Banach space valued random variables ⋮ A supplement to the laws of large numbers and the large deviations ⋮ On the convergence of vector random measures ⋮ Central limit theorem for stochastically continuous processes. Convergence to stable limit ⋮ On the (p,q)$(p,q)$‐type strong law of large numbers for sequences of independent random variables ⋮ Unnamed Item ⋮ Optimal moment conditions for complete convergence for maximal normed weighted sums from arrays of rowwise independent random elements in Banach spaces ⋮ Weak laws of large numbers of double sums of independent random elements in Rademacher type \(p\) and stable type \(p\) Banach spaces ⋮ A family of stable measures in some Banach spaces ⋮ A refinement of the Kolmogorov-Marcinkiewicz-Zygmund strong law of large numbers ⋮ Mean convergence theorem for multidimensional arrays of random elements in Banach spaces ⋮ On the weak laws of large numbers for weighted sums of dependent identically distributed random vectors in Hilbert spaces ⋮ Law of large numbers for identically distributed Banach-valued random variables ⋮ The Marcinkiewicz-Zygmund LLN in Banach spaces: a generalized martingale approach ⋮ Operators generating stable measures on banach spaces ⋮ Tercentennial anniversary of Bernoulli’s law of large numbers ⋮ Operators of stable type ⋮ Operator ideal of type (p,q) ⋮ Central limit theorems and weak laws of large numbers in certain banach spaces ⋮ Uniform and universal Glivenko-Cantelli classes ⋮ A note on dichotomy theorems for integrals of stable processes

Cites Work

• Uniform convergence of random Fourier series
• Sous-espaces de dimension finie des espaces de Banach reticules
• The law of large numbers and the central limit theorem in Banach spaces
• A Convexity Condition in Banach Spaces and the Strong Law of Large Numbers
• Zero-One Laws for Stable Measures
• Domains of attraction of stable measures on a Hilbert space
• Integrability of Infinite Sums of Independent Vector-Valued Random Variables
• Lois e(?) dans les espaces vectoriels et lois stables
• Séries de variables aléatoires vectorielles indépendantes et propriétés géométriques des espaces de Banach
• A convergence of types theorem for probability measures on topological vector spaces with applications to stable laws
• Harmonic Analysis on Certain Vector Spaces
• Sums of independent Banach space valued random variables
• 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

This page was built for publication: Stable Measures and Central Limit Theorems in Spaces of Stable Type