Complete convergence of stochastic approximation algorithm in Rd under random noises

被引：2

作者：

Arab, Idir ^{[1
]}

Dahmani, Abdelnasser ^{[2
]}

机构：

[1] Univ A MIRA Bejaia, Fac Sci Exactes, Lab Math Appl, Bejaia 06000, Algeria

[2] Ctr Univ Tamanrasset, Tamanrasset, Algeria

来源：

SEQUENTIAL ANALYSIS-DESIGN METHODS AND APPLICATIONS | 2016年 / 35卷 / 02期

关键词：

Bernstein inequalities; dependent noise; exponential bounds; independent noise; quasi-associated random variables; root of a function; stochastic approximation; RANDOM-VARIABLES; ROBBINS-MONRO; INEQUALITIES;

D O I：

10.1080/07474946.2016.1165537

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

In this article, we study a stochastic approximation algorithm that approximates the exact root theta of a function M defined in R-d into R-d. The function M cannot be known exactly, but only noisy measurements are available at each point x(n) with the error xi(n). The sequence of noise (xi(n))(n) is random; we treat both cases where it is independent and dependent and we establish the complete convergence of the approximated sequence of theta.

引用

页码：216 / 225

页数：10

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