Complete convergence of martingale arrays
type: Item
instance of: scholarly article
title: Complete convergence of martingale arrays
zbMATH Open document ID: 0913.60029
DOI: 10.1023/A:1022646429754
author: Subhashis Ghosal
author: Tapas K. Chandra
published in: Journal of Theoretical Probability
publication date: 1999-06-01T00:00:00Z
review text: A sequence \(\{U_n, n\geq 1\}\) of random variables is said to converge completely to the constant \(c\) if \(\sum^\infty_{n= 1} P(| U_n- c|> \varepsilon)< \infty\) for all \(\varepsilon> 0\). The definition was introduced by \textit{P. L. Hsu} and \textit{H. Robbins} [Proc. Natl. Acad. Sci. USA 33, 25-31 (1947; Zbl 0030.20101)], and the authors also proved a result on complete convergence in the law of large numbers. The present paper is an extension to complete convergence for square-integrable martingale arrays together with several examples.
reviewed by: Allan Gut
Mathematics Subject Classification ID: 60F15
Mathematics Subject Classification ID: 60G42
zbMATH DE Number: 1208775
zbMATH Keywords: complete convergence
zbMATH Keywords: law of large numbers
zbMATH Keywords: square-integrable martingale arrays
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1208775