Limit distributions and one-parameter groups of linear operators on Banach spaces

DOI10.1016/0047-259X(83)90042-8zbMath0533.60004MaRDI QIDQ789801

Zbigniew J. Jurek

Publication date: 1983

Published in: Journal of Multivariate Analysis (Search for Journal in Brave)

zbMATH Keywords

one parameter semigroupGaussian covariance operatorgeneralized Poisson exponentLévy and Urbanik classes of infinitely divisible measures

Mathematics Subject Classification ID

Probability measures on topological spaces (60B05) Central limit and other weak theorems (60F05) Convergence of probability measures (60B10)

Related Items (14)

Completely operator-selfdecomposable distributions and operator-stable distributions ⋮ A new factorization property of the selfdecomposable probability measures. ⋮ Exponential bounds of ruin probabilities for non-homogeneous risk models ⋮ Random integral representations for classes of limit distributions similar to Lévy class \(L_ 0\) ⋮ Operator self-similar processes on Banach spaces ⋮ The random integral representation conjecture: a quarter of a century later ⋮ Some definite integrals arising from selfdecomposable characteristic functions ⋮ Which Urbanik class \(L_k\), do the hyperbolic and the generalized logistic characteristic functions belong to? ⋮ Selfdecomposability of moving average fractional Lévy processes ⋮ Three classes of decomposable distributions ⋮ Operator-selfdecomposable distributions as limit distributions of processes of Ornstein-Uhlenbeck type ⋮ MatG Random Matrices ⋮ An integral representation for selfdecomposable banach space valued random variables ⋮ An alternative approach to multiply self-decomposable probability measures on Banach spaces

Cites Work

• Multiply monotone functions and their Laplace transforms
• Class L of multivariate distributions and its subclasses
• Structure of a class of operator-selfdecomposable probability measures
• Representation of certain infinitely divisible probability measures on Banach spaces
• Characterization of subclasses of class L probability distributions
• Operator-stable probability measures on Banach spaces
• Remarks on stable measures on Banach spaces
• Lévy's probability measures on Banach spaces
• Self-decomposable probability measures on Banach spaces
• Stable probability measures on Banach spaces
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