One-dimensional uniqueness and convergence criteria for exchangeable processes
type: Item
instance of: scholarly article
title: One-dimensional uniqueness and convergence criteria for exchangeable processes
zbMATH Open document ID: 0645.60041
DOI: 10.1016/0304-4149(88)90095-6
author: Olav Kallenberg
published in: Stochastic Processes and their Applications
publication date: 1988-01-01T00:00:00Z
review text: If X and Y are exchangeable processes on \(I=[0,1]\) or \(R_+\); and \(X_ t\) and \(Y_ t\) have the same distribution for all t in certain infinite time-sets then, under suitable moment conditions, it is shown that \(X_ t\) and \(Y_ t\) have the same distribution for all t. The proof relies on the analytic properties of the characteristic functions of exchangeable processes. This result is used to prove the main theorem that if X, \(X_ 1\), \(X_ 2\),... are exchangeable processes on I or \(R_+\) and \(X_ n(t)\) converges in distribution to X(t) for all t in some suitable subset of I or \(R_+\) then \(X_ n\) converges in distribution to X, provided X is continuous or ergodic and satisfies certain moment conditions.
Mathematics Subject Classification ID: 60G09
Mathematics Subject Classification ID: 60F17
Mathematics Subject Classification ID: 60J99
zbMATH DE Number: 4052691
zbMATH Keywords: local limit theorems
zbMATH Keywords: convergence in distribution
zbMATH Keywords: exchangeable processes
zbMATH Keywords: characteristic functions of exchangeable processes
zbMATH Keywords: moment conditions
reviewed by: Neville Weber
MaRDI profile type: Publication
full work available at URL: 0304-4149(88)90095-6
OpenAlex ID: W2013195574
cites work: Q3675249
cites work: Q5560061
cites work: Q3915688
cites work: École d'été de probabilités de Saint-Flour XIII - 1983
cites work: Q3679996
cites work: Canonical representations and convergence criteria for processes with interchangeable increments
cites work: Path properties of processes with independent and interchangeable increments
cites work: On Symmetrically Distributed Random Measures
cites work: Characterizations and embedding properties in exchangeability
cites work: Q4776689
cites work: Spreading and predictable sampling in exchangeable sequences and processes
cites work: Q4131338
cites work: Q5598785
cites work: Q3821337
description: scientific article; zbMATH DE number 4052691