Random integral representations for classes of limit distributions similar to Lévy class \(L_ 0\)

DOI10.1007/BF00334208zbMath0628.60009OpenAlexW4235555051MaRDI QIDQ1093232

Zbigniew J. Jurek

Publication date: 1988

Published in: Probability Theory and Related Fields (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00334208

zbMATH Keywords

convolution equationsinfinitely divisible measuresSkorohod topologyLévy classrandom integral functionals

Mathematics Subject Classification ID

Infinitely divisible distributions; stable distributions (60E07) Probability distributions: general theory (60E05) Stochastic integrals (60H05) Limit theorems for vector-valued random variables (infinite-dimensional case) (60B12)

Related Items (17)

Exponential bounds of ruin probabilities for non-homogeneous risk models ⋮ Inversions of infinitely divisible distributions and conjugates of stochastic integral mappings ⋮ Random integral representations for free-infinitely divisible and tempered stable distributions ⋮ \(\alpha \)-selfdecomposable distributions and related Ornstein-Uhlenbeck type processes ⋮ A note on a bivariate gamma distribution ⋮ The random integral representation conjecture: a quarter of a century later ⋮ Nested subclasses of the class of \(\alpha\)-selfdecomposable distributions ⋮ Classes of infinitely divisible distributions on \(\mathbb R^d\) related to the class of selfdecomposable distributions ⋮ Quantile clocks ⋮ Fourier transforms of measures from the classes \({\mathcal U}_ \beta{},\;-2 < \beta{}\leq{}-1\) ⋮ Random integral representations for classes of limit distributions similar to Lévy class L₀, II ⋮ A random integral calculus on generalized \(s\)-selfdecomposable probability measures ⋮ Fixed points of mappings of infinitely divisible distributions on ⋮ Semigroups of Upsilon transformations ⋮ Classes of Infinitely Divisible Distributions and Examples ⋮ Fractional Integrals and Extensions of Selfdecomposability ⋮ A Note on a Composition of Two Random Integral Mappings ^βand Some Examples

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Limit distributions and one-parameter groups of linear operators on Banach spaces
• Operator-selfdecomposable distributions as limit distributions of processes of Ornstein-Uhlenbeck type
• Relations between the \(\epsilon\)-selfdecomposable and selfdecomposable measures
• Class L of multivariate distributions and its subclasses
• On a continuous analogue of the stochastic difference equation \(X_ n\) = rho X//(n-1) + \(B_ n\).
• An integral representation for selfdecomposable banach space valued random variables
• Infinitely divisible distributions similar to class L distributions
• Weak convergence of probability measures and random functions in the function space D[0,∞)
• Convergence of stochastic processes

This page was built for publication: Random integral representations for classes of limit distributions similar to Lévy class \(L_ 0\)