A central limit theorem for D(A)-valued processes
type: Item
instance of: scholarly article
title: A central limit theorem for D(A)-valued processes
zbMATH Open document ID: 0617.60020
DOI: 10.1016/0304-4149(87)90032-9
author: Richard F. Bass
author: Ronald Pyke
published in: Stochastic Processes and their Applications
publication date: 1987-01-01T00:00:00Z
review text: Let D(A) be the space of set-indexed functions that are outer continuous with inner limits, a generalization of D[0,1]. This paper proves a central limit theorem (CLT) for triangular arrays of independent D(A)- valued random variables. The limit processes are not restricted to be Gaussian, but can be quite general infinitely divisible processes. This is an important result with a basic and essential sense for the functional limit theory. Applications of this CLT include construction of set-indexed Levy processes and a unified CLT for partial sum processes and generalized empirical processes. Results obtained by this way are new even for the D[0,1] case.
reviewed by: Chun Su
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 60F17
Mathematics Subject Classification ID: 60B12
zbMATH DE Number: 4001087
zbMATH Keywords: Skorohod topology
zbMATH Keywords: set-indexed functions
zbMATH Keywords: central limit theorem
zbMATH Keywords: triangular arrays
zbMATH Keywords: infinitely divisible processes
zbMATH Keywords: set-indexed Levy processes
zbMATH Keywords: empirical processes
MaRDI profile type: Publication
full work available at URL: 0304-4149(87)90032-9
OpenAlex ID: W1976906054
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description: scientific article; zbMATH DE number 4001087