Convergence of stochastic approximation procedures with dependent noise (Q1262667)

This paper studies the convergence of a Robbins-Monro stochastic approximation procedure with dependent noise in the mean of order \(p\geq 2\) and with probability one. Sufficient conditions for convergence are derived. The proof of the convergence is based on convergence of a series of dependent random variables and mean convergence of a weighted sum of dependent random variables relating to linearization of the original procedure [\textit{A. S. Poznyak} and the author, Autom. Remote Control 45, 1601-1615 (1984); translation from Avtom. Telemekh. 1984, No.12, 78-93 (1984; Zbl 0603.62091)].