Divergence Processes and Weak Convergence of Likelihood Ratio Processes
Doubly stochastic compound Poisson processes in extreme value theory.
Dynamics of Stochastic Neuronal Networks and the Connections to Random Graph Theory
We analyze a stochastic neuronal network model which corresponds to an all-to-all network of discretized integrate-and-fire neurons where the synapses are failure-prone. This network exhibits different phases of behavior corresponding to synchrony and asynchrony, and we show that this is due to the limiting mean-field system possessing multiple attractors. We also show that this mean-field limit exhibits a first-order phase transition as a function...
Edgeworth expansions for a sample sum from a finite set of independent random variables.
Effective WLLN, SLLN and CLT in statistical models
Weak laws of large numbers (WLLN), strong laws of large numbers (SLLN), and central limit theorems (CLT) in statistical models differ from those in probability theory in that they should hold uniformly in the family of distributions specified by the model. If a limit law states that for every ε > 0 there exists N such that for all n > N the inequalities |ξₙ| < ε are satisfied and N = N(ε) is explicitly given then we call the law effective. It is trivial to obtain an effective statistical...
Einführung des Wahrscheinlichkeitsoperators durch Postulate.
Entropie, théorèmes limite et marches aléatoires
Ergodic and central limit theorems in statistical mechanics in continuous case
Error bounds on the non-normal approximation of Hermite power variations of fractional Brownian motion.
Error estimates in -dimensional renewal theory
Estimates for the distribution of sums and maxima of sums of random variables without the Cramér condition.
Estimates in the invariance principle in terms of truncated power moments.
Estimates of the rate of approximation in a de-poissonization lemma
Estimating a Distribution Function in the Presence of Auxiliary Information.
Estimation in models driven by fractional brownian motion
Let {bH(t), t∈ℝ} be the fractional brownian motion with parameter 0<H<1. When 1/2<H, we consider diffusion equations of the type X(t)=c+∫0tσ(X(u)) dbH(u)+∫0tμ(X(u)) du. In different particular models where σ(x)=σ or σ(x)=σ x and μ(x)=μ or μ(x)=μ x, we propose a central limit theorem for estimators of H and of σ based on regression methods. Then we give tests of the hypothesis on σ for these models. We also consider functional estimation on σ(⋅)...
Estimation of a quadratic functional of a density.
Étude asymptotique du temps passé par le mouvement brownien dans un cône
Étude asymptotique d'une marche aléatoire centrifuge
Étude de l'estimateur du maximum de vraisemblance dans le cas d'un processus autorégressif : convergence, normalité asymptotique, vitesse de convergence
Étude d’une transformation non uniformément hyperbolique de l’intervalle
Nous étudions un exemple de transformation non uniformément hyperbolique de l’intervalle . Des exemples analogues ont été étudiés par de nombreux auteurs. Notre méthode utilise une théorie spectrale, pour une classe d’opérateurs vérifiant des conditions faibles de Doeblin-Fortet, introduite dans [1]. Elle nous permet, en particulier, de donner une estimation de la vitesse de décroissance des corrélations pour des fonctions non höldériennes.