Limit theorems for random vectors with operator normalizations. II
type: Item
instance of: scholarly article
zbMATH Open document ID: 1004.60027
author: V. O. Koval'
publication date: 2001-09-11T00:00:00Z
Mathematics Subject Classification ID: 60F15
Mathematics Subject Classification ID: 60G42
Mathematics Subject Classification ID: 60G35
zbMATH DE Number: 1645093
zbMATH Keywords: operator normalized random vectors
zbMATH Keywords: limit theorems
zbMATH Keywords: martingales
zbMATH Keywords: autoregression process
zbMATH Keywords: strong law of large numbers
zbMATH Keywords: operator normalization
zbMATH Keywords: sub-Gaussian martingales
MaRDI profile type: Publication
title: Limit theorems for random vectors with operator normalizations. II
published in: Teoriya Ĭmovirnosteĭ ta Matematychna Statystyka
review text: This article is the second part of the article [Theory Probab. Math. Stat. 61, 49-60 (2000); translation from Teor. Jmovirn. Mat. Stat. 61, 47-58 (1999; Zbl 0986.60021)]. The strong law of large numbers with operator normalization for sub-Gaussian martingales is studied and its application to the investigation of the asymptotic properties of many-dimensional autoregression processes is given. Conditions of fulfillment of the strong law of large numbers with operator normalization for vector sub-Gaussian martingales are proposed. In the one-dimensional case the sub-Gaussian martingales were studied by \textit{K. Azuma} [Tôhoku Math. J., II. Ser. 19, 357-367 (1967; Zbl 0178.21103)] and \textit{W. F. Stout} [``Almost sure convergence'' (1974; Zbl 0321.60022)].
description: scientific article; zbMATH DE number 1645093