Limit theorems for probability measures on simply connected nilpotent Lie groups

DOI10.1007/BF01258737zbMath0722.60011OpenAlexW1979353504WikidataQ115393771 ScholiaQ115393771MaRDI QIDQ756234

Siegfried Nobel

Publication date: 1991

Published in: Journal of Theoretical Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01258737

zbMATH Keywords

nilpotent Lie grouplocally compact groupcontinuous one-parameter semigroupdifferent types of domains of attractionstability of probability measures

Mathematics Subject Classification ID

Infinitely divisible distributions; stable distributions (60E07) Convergence of probability measures (60B10) Probability measures on groups or semigroups, Fourier transforms, factorization (60B15)

Related Items (14)

\({\mathcal D}\)-domains of attraction of stable measures on stratified Lie groups ⋮ A Gaussian central limit theorem for trimmed products on simply connected step 2-nilpotent Lie groups ⋮ Über den Typenkonvergenzsatz auf zusammenhängenden Lie Gruppen. (On the convergence-of-types-theorem on connected Lie groups) ⋮ The accuracy of Gaussian approximations in nilpotent Lie groups ⋮ Moments of measures attracted to operator semi-stable laws ⋮ Domains of attraction of stable semigroups on simply connected nilpotent Lie groups ⋮ Uniqueness of embedding of Gaussian probability measures into a continuous convolution semigroup on simply connected nilpotent Lie groups ⋮ Semistable Selfdecomposable Laws on Groups ⋮ Semistable measures and limit theorems on real and \(p\)-adic groups ⋮ Uniqueness of embedding into a Gaussian semigroup and a Poisson semigroup with determinate jump law on a simply connected nilpotent Lie group ⋮ Embeddability of infinitely divisible distributions on linear Lie groups ⋮ The domains of partial attraction of probabilities on groups and on vector spaces ⋮ The Prokhorov-Loève law of large numbers on countable subgroups of simply connected step 2-nilpotent Lie groups ⋮ Some new limit theorems for vector space- and group-valued random variables

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Semistable convolution semigroups on measurable and topological groups
• Elliptical symmetry and characterization of operator-stable and operator semi-stable measures
• Domains of operator semi-attraction of operator semi-stable probability measures
• Unicité du plongement d'une mesure de probabilité dans un semi-groupe de convolution gaussien. Cas non-abélien
• Continuous automorphism groups on a locally compact group contracting modulo a compact subgroup and applications to stable convolution semigroups
• Supplements to operator-stable and operator-semistable laws on Euclidean spaces
• Automorphisms on a Lie group contracting modulo a compact subgroup and applications to semistable convolution semigroups
• Fourier analysis and limit theorems for convolution semigroups on a locally compact group
• Strongly Operator‐Decomposable Probability Measures on Separable Banach Spaces
• Limit theorems for probability measures on non-compact groups and semi-groups
• Semi-stable probability measures on $R^{N}$
• Infinitely Divisible Distributions on Connected Nilpotent Lie Groups
• On the Extension of the Class of Stable Distributions
• Operator-Stable Probability Distributions on Vector Groups
• Lévy's probability measures on Euclidean spaces
• Einbettung unendlich teilbarer Wahrscheinlichkeitsma\e auf topologischen Gruppen

This page was built for publication: Limit theorems for probability measures on simply connected nilpotent Lie groups