A general principle for limit theorems in finitely additive probability: The dependent case
type: Item
instance of: scholarly article
title: A general principle for limit theorems in finitely additive probability: The dependent case
zbMATH Open document ID: 0638.60026
DOI: 10.1016/0047-259X(88)90035-8
published in: Journal of Multivariate Analysis
publication date: 1988-01-01T00:00:00Z
review text: In Trans. Am. Math. Soc. 273, 541-550 (1982; Zbl 0507.60012), the author has proved a general principle, i.e. almost all limit theorems that are true in countably additive probability theory are also true in finitely additive probability theory in the independent case. Here, this result is generalized to the dependent case on the same line. More precisely, given a sequence \(\{Y_ n\}\) of random variables on a finitely additive probability space, one can construct a sequence \(\{X_ n\}\) of random variables on a countably additive probability space such that a convergence in probability or in distribution type limit theorem holds for \(\{Y_ n\}\) iff it holds for \(\{X_ n\}\). If the sequence \(\{Y_ n\}\) satisfies further an additional condition, the same is true for a.s. convergence type limit theorems.
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 60G07
zbMATH DE Number: 4040935
zbMATH Keywords: martingales
zbMATH Keywords: exchangeable sequences
zbMATH Keywords: subsequence principle
zbMATH Keywords: finitely additive probability theory
author: Rajeeva L. Karandikar
reviewed by: Zhengyan Lin
MaRDI profile type: Publication
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full work available at URL: 0047-259x(88)90035-8
OpenAlex ID: W1976089207
description: scientific article; zbMATH DE number 4040935