L'approximation stochastique en analyse des correspondances
Learning extremal regulator implementation by a stochastic automaton and stochastic approximation theory
There exist many different approaches to the investigation of the characteristics of learning system. These approaches use different branches of mathematics and, thus, obtain different results, some of them are too complicated and others do not match the results of practical experiments. This paper presents the modelling of learning systems by means of stochastic automate, mainly one particular model of a learning extremal regulator. The proof of convergence is based on Dvoretzky's Theorem on stochastic...
Les algorithmes stochastiques contournent-ils les pièges ?
Non-Asymptotic Confidence Bounds for Stochastic Approximation Algorithms with Constant Step Size.
Notes on stochastic approximation methods
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
Parametric inference for mixed models defined by stochastic differential equations
Non-linear mixed models defined by stochastic differential equations (SDEs) are considered: the parameters of the diffusion process are random variables and vary among the individuals. A maximum likelihood estimation method based on the Stochastic Approximation EM algorithm, is proposed. This estimation method uses the Euler-Maruyama approximation of the diffusion, achieved using latent auxiliary data introduced to complete the diffusion process between each pair of measurement instants. A tuned...
Particle approximations of Lyapunov exponents connected to Schrödinger operators and Feynman–Kac semigroups
We present an interacting particle system methodology for the numerical solving of the Lyapunov exponent of Feynman–Kac semigroups and for estimating the principal eigenvalue of Schrödinger generators. The continuous or discrete time models studied in this work consists of interacting particles evolving in an environment with soft obstacles related to a potential function . These models are related to genetic algorithms and Moran type particle schemes. Their choice is not unique. We will examine...
Particle approximations of Lyapunov exponents connected to Schrödinger operators and Feynman–Kac semigroups
We present an interacting particle system methodology for the numerical solving of the Lyapunov exponent of Feynman–Kac semigroups and for estimating the principal eigenvalue of Schrödinger generators. The continuous or discrete time models studied in this work consists of N interacting particles evolving in an environment with soft obstacles related to a potential function V. These models are related to genetic algorithms and Moran type particle schemes. Their choice is not unique. We...