O stochastické aproximaci
On a class of discrete generation interacting particle systems.
On a Stochastic Approximation Procedure Based on Averaging.
On Bather's stochastic approximation algorithm
On estimation of a covariance function of stationary errors in a nonlinear regression model.
On integer stochastic approximation
Let be observable, with experimental errors, at integer points only; unknown elsewhere. Iterative nonparametric procedures for finding the zero point of are called procedures of integer stochastic approximation. Three types of such procedures (Derman’s, Mukerjee’s and the authors’) are described and compared. A two-dimensional analogue of the third approach is proposed and investigated; its generalization to higher dimensions is conjectured.
On the convergence of moments in the almost sure central limit theorem for stochastic approximation algorithms
We study the almost sure asymptotic behaviour of stochastic approximation algorithms for the search of zero of a real function. The quadratic strong law of large numbers is extended to the powers greater than one. In other words, the convergence of moments in the almost sure central limit theorem (ASCLT) is established. As a by-product of this convergence, one gets another proof of ASCLT for stochastic approximation algorithms. The convergence result is applied to several examples as estimation...
On the convergence of the dynamic stochastic approximation method for stochastic non-linear multidimensional dynamic systems
On the dynamic stochastic approximation
On the Recursive Estimation of the Location and of the Size of the Mode of a Probability Density
2000 Mathematics Subject Classification: 62G07, 62L20.Tsybakov [31] introduced the method of stochastic approximation to construct a recursive estimator of the location q of the mode of a probability density. The aim of this paper is to provide a companion algorithm to Tsybakov's algorithm, which allows to simultaneously recursively approximate the size m of the mode. We provide a precise study of the joint weak convergence rate of both estimators. Moreover, we introduce the averaging principle...
On the stability of interacting processes with applications to filtering and genetic algorithms