Convergence in probability and almost sure with applications.
type: Item
instance of: scholarly article
title: Convergence in probability and almost sure with applications.
zbMATH Open document ID: 1053.60092
DOI: 10.1016/S0304-4149(01)00075-8
author: Harry Cohn
published in: Stochastic Processes and their Applications
publication date: 2004-11-26T00:00:00Z
review text: The paper investigates convergence in probability of an adapted real-valued stochastic process when the time is tending to infinity. Provided convergence in law, the author presents conditions equivalent to the convergence in probability. Moreover, an almost surely convergent process is constructed in that case. The result generalizes the well-known convergence property of martingales.
Mathematics Subject Classification ID: 60J80
zbMATH DE Number: 2119511
zbMATH Keywords: martingale
zbMATH Keywords: slow variation
zbMATH Keywords: varying environment
zbMATH Keywords: branching random walks
zbMATH Keywords: weighted sums
zbMATH Keywords: weak laws
reviewed by: Petr Lachout
MaRDI profile type: Publication
cites work: Q5674726
cites work: Chernoff's theorem in the branching random walk
cites work: Seneta-Heyde norming in the branching random walk
cites work: Multi-type branching in varying environment
cites work: Q5284179
cites work: Q4040465
cites work: Almost sure convergence of branching processes
cites work: On a property related to convergence in probability and some applications to branching processes
cites work: A martingale approach to supercritical (CMJ) branching processes
cites work: On the growth of the multitype supercritical branching process in a random environment
cites work: Q4840710
cites work: On the limit behaviour of weighted sums of random variables
cites work: General branching processes in varying environment
cites work: Q3999383
cites work: Q5624436
cites work: Limit theorems for the supercritical Galton-Watson process in varying environments
cites work: Q4361716
cites work: Extension of a Result of Seneta for the Super-Critical Galton-Watson Process
cites work: Supercritical multitype branching processes
cites work: Convergence of weighted averages of independent random variables
cites work: On the convergence of multitype branching processes with varying environments
cites work: On the convergence of supercritical general (C-M-J) branching processes
cites work: Q4327561
cites work: On the asymptotic behaviour of branching processes with infinite mean
cites work: On Recent Theorems Concerning the Supercritical Galton-Watson Process
Wikidata QID: Q126353075
description: scientific article; zbMATH DE number 2119511