On the almost sure asymptotic behaviour of stochastic algorithm
type: Item
instance of: scholarly article
title: On the almost sure asymptotic behaviour of stochastic algorithm
zbMATH Open document ID: 0926.62072
DOI: 10.1016/S0304-4149(98)00029-5
author: Mariane Pelletier
published in: Stochastic Processes and their Applications
publication date: 1999-11-18T00:00:00Z
review text: The author considers a stochastic algorithm of the form: \( Z_{n+1}=Z_n +\gamma_n(h(Z_n)+r_n)+ \sigma_n \epsilon_{n+1},\) where \(h :R^d \to R^d,\) \(\{r_n\}\) and \(\{\epsilon_n\}\) are disturbances and \(\{\gamma_n\}\) , \(\{\sigma_n\}\) are nonrandom strictly positive sequences with \(\sum_n\gamma_n<\infty\), \(\sum_n\sigma_n<\infty \). She studies almost sure behavior of the algorithm. A law of iterated logarithm and a quadratic strong law of large numbers are established.
Mathematics Subject Classification ID: 62L20
Mathematics Subject Classification ID: 60F15
Mathematics Subject Classification ID: 60F05
zbMATH DE Number: 1364522
zbMATH Keywords: stochastic algorithm
zbMATH Keywords: laws of iterated logarithm
zbMATH Keywords: quadratic laws of large numbers
reviewed by: Marie Hušková
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1364522