Operator-selfdecomposable distributions as limit distributions of processes of Ornstein-Uhlenbeck type
type: Item
instance of: scholarly article
title: Operator-selfdecomposable distributions as limit distributions of processes of Ornstein-Uhlenbeck type
zbMATH Open document ID: 0533.60021
DOI: 10.1016/0304-4149(84)90312-0
author: Ken-Iti Sato
author: Makoto Yamazato
published in: Stochastic Processes and their Applications
publication date: 1984-01-01T00:00:00Z
review text: A random variable X is said to have an operator-selfdecomposable or Lévy distribution if there are sequences \(\{X_ n\}\), \(\{A_ n\}\) and \(\{a_ n\}\) of respectively independent random variables, linear operators, and vectors such that the random variables \(A_ n(X_ 1+...+X_ n)-a_ n\) converge completely to X and in addition an infinitesimal condition is satisfied. Processes of Ornstein-Uhlenbeck type on Euclidean spaces are analogues of the Ornstein-Uhlenbeck process with the Brownian motion part replaced by general processes with homogeneous independent increments. The class of operator- selfdecomposable distributions is characterized as the class of limit distributions of processes of Ornstein-Uhlenbeck type. Integro- differential equations for operator-selfdecomposable distributions are established.
Mathematics Subject Classification ID: 60E07
Mathematics Subject Classification ID: 60J25
zbMATH DE Number: 3846550
zbMATH Keywords: infinitely divisible distribution
zbMATH Keywords: OL distribution
zbMATH Keywords: operator- selfdecomposable distribution
zbMATH Keywords: process of Ornstein-Uhlenbeck type
MaRDI profile type: Publication
full work available at URL: 0304-4149(84)90312-0
OpenAlex ID: W2061416793
cites work: Stationary distributions for dams with additive input and content-dependent release rate
cites work: A stochastic integral in storage theory
cites work: Q4137812
cites work: Q5342182
cites work: Q4086490
cites work: Operator-stable laws
cites work: Operator-stable distribution on \(R^ 2\) with multiple exponents
cites work: Structure of a class of operator-selfdecomposable probability measures
cites work: Q3969648
cites work: Limit distributions and one-parameter groups of linear operators on Banach spaces
cites work: An integral representation for selfdecomposable banach space valued random variables
cites work: Q3843987
cites work: Q5533878
cites work: Q4765784
cites work: Class L of multivariate distributions and its subclasses
cites work: Absolute continuity of multivariate distributions of class L
cites work: On distribution functions of class L
cites work: Q3314684
cites work: Operator-Stable Probability Distributions on Vector Groups
cites work: Q5798928
cites work: Q5641908
cites work: Lévy's probability measures on Euclidean spaces
cites work: A limit theorem of branching processes and continuous state branching processes
cites work: On the Continuity Properties of $L$ Functions
cites work: On the unimodality of multivariate symmetric distribution functions of class L
cites work: A characterization of Levy probability distribution functions on Euclidean spaces
cites work: On a continuous analogue of the stochastic difference equation \(X_ n\) = rho X//(n-1) + \(B_ n\).
cites work: Unimodality of infinitely divisible distribution functions of class L
cites work: Q3313022
cites work: Q3935206
description: scientific article; zbMATH DE number 3846550