Pathwise approximations of processes based on the fine structure of their filtrations
Přehled deterministických a stochastických aproximačních metod pro minimalizaci funkcí
Processus de branchements dépendant de la densité, markovien en temps continu
Quadratic mean and almost-sure convergence of unbounded stochastic approximation algorithms with correlated observations
Quasi-Isotonic Regression and Stochastic Approximation.
Reconnaissance des formes. Apprentissage et approximation stochastique
Recursive estimates of quantile based on 0-1 observations
The objective of this paper is to introduce some recursive methods that can be used for estimating an value. These methods can be used more generally for the estimation of the -quantile of an unknown distribution provided we have 0-1 observations at our disposal. Standard methods based on the Robbins-Monro procedure are introduced together with different approaches of Wu or Mukerjee. Several examples are also mentioned in order to demonstrate the usefulness of the methods presented.
Recursive estimation as an optimally controlled process
Résolution adaptative de l'équation de Wiener-Hopf. Cas d'un canal de données affecté de gigue
Sequential estimation of survival functions with a neutral to the right process prior
In this work, a parametric sequential estimation method of survival functions is proposed in the Bayesian nonparametric context when neutral to the right processes are used. It is proved that the mentioned method is an 1-SLA rule when Dirichlet processes are used; furthermore, asymptotically pointwise optimal procedures are obtained. Finally, an example is given.
Some Results About Averaging in Stochastic Approximation.
Stetige stochastische Approximation.
Stochastic approximations in the presence of trend
Stochastic approximations of the solution of a full Boltzmann equation with small initial data
Stochastic approximations of the solution of a full Boltzmann equation with small initial data
This paper gives an approximation of the solution of the Boltzmann equation by stochastic interacting particle systems in a case of cut-off collision operator and small initial data. In this case, following the ideas of Mischler and Perthame, we prove the existence and uniqueness of the solution of this equation and also the existence and uniqueness of the solution of the associated nonlinear martingale problem. Then, we first delocalize the interaction by considering a mollified Boltzmann...
Sur quelques algorithmes récursifs pour les probabilités numériques
The aim of this paper is to take an in-depth look at the long time behaviour of some continuous time markovian dynamical systems and at its numerical analysis. We first propose a short overview of the main ergodicity properties of time continuous homogeneous Markov processes (stability, positive recurrence). The basic tool is a Lyapunov function. Then, we investigate if these properties still hold for the time discretization of these processes, either with constant or decreasing step (ODE method...
Sur quelques algorithmes récursifs pour les probabilités numériques
The aim of this paper is to take an in-depth look at the long time behaviour of some continuous time Markovian dynamical systems and at its numerical analysis. We first propose a short overview of the main ergodicity properties of time continuous homogeneous Markov processes (stability, positive recurrence). The basic tool is a Lyapunov function. Then, we investigate if these properties still hold for the time discretization of these processes, either with constant or decreasing step (ODE...
Sur quelques résultats asymptotiques pour le processus de Robbins-Monro
The continuous dynamic Robbins-Monro procedure
The N-Armed Bandit with Unimodal Structure.