The space D(A) and weak convergence for set-indexed processes
type: Item
instance of: scholarly article
title: The space D(A) and weak convergence for set-indexed processes
zbMATH Open document ID: 0585.60007
author: Richard F. Bass
author: Ronald Pyke
published in: The Annals of Probability
publication date: 1985-01-01T00:00:00Z
review text: A topology is introduced for the space D(A) of functions which are outer continuous with inner limits indexed by a family of Borel subsets of the d-dimensional unit cube. The space is a natural extension of D[0,1] as a range space of sample paths for processes indexed by a family of sets. Weak convergence of such processes is considered. The topology is similar in spirit to the \(M_ 2\) topology of Skorokhod for D[0,1] in that the distance between two functions is defined by the Hausdorff distance between their graphs. A central limit theorem for partial-sum processes indexed by a family of sets is established.
Mathematics Subject Classification ID: 60B10
Mathematics Subject Classification ID: 60F17
Mathematics Subject Classification ID: 60B05
zbMATH DE Number: 3938122
zbMATH Keywords: Weak convergence
zbMATH Keywords: topology of Skorokhod
zbMATH Keywords: Hausdorff distance
zbMATH Keywords: central limit theorem
reviewed by: D. P. Kennedy
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aop/1176992911
OpenAlex ID: W2072877209
DOI: 10.1214/AOP/1176992911
description: scientific article; zbMATH DE number 3938122