Complete convergence of stochastic approximation algorithm in ℝd under random noises. Issue 2 (2nd April 2016)

• Record Type: Journal Article
• Authors: Arab, Idir; Dahmani, Abdelnasser
• Is Part Of: Sequential analysis. Volume 35:Issue 2(2016)
• Page Start: 216
• Page End: 225
• Publication Date: 2016-04-02
• Subjects: Bernstein inequalities -- dependent noise -- exponential bounds -- independent noise -- quasi-associated random variables -- root of a function -- stochastic approximation; 15A06 -- 15A29 -- 60E15 -- 60F15 -- 62H20 -- 62L10; Sequential analysis -- Periodicals; 519.54
• DOI: 10.1080/07474946.2016.1165537
• Languages: English
• ISSNs: 0747-4946

Abstract

ABSTRACT: In this article, we study a stochastic approximation algorithm that approximates the exact root θ 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 ξ n . The sequence of noise (ξ 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 θ.