Estimation de la densité du recuit simulé
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.
Estimations de grandes déviations pour des systèmes où apparaissent un bruit Gaussien et un bruit non Gaussien
Estimations de la dimension inférieure et de la dimension supérieure des mesures
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 des extrêmes d'une suite stationnaire m-dépendante avec une application relative aux accroissements du processus de Wiener
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.
Euclidean distances on signed measures and application to Berry-Esséen theorems. (Distances euclidiennes sur les mesures signées et application à des théorèmes de Berry-Esséen.)
Euler's Approximations of Solutions of Reflecting SDEs with Discontinuous Coefficients
Let D be either a convex domain in or a domain satisfying the conditions (A) and (B) considered by Lions and Sznitman (1984) and Saisho (1987). We investigate convergence in law as well as in for the Euler and Euler-Peano schemes for stochastic differential equations in D with normal reflection at the boundary. The coefficients are measurable, continuous almost everywhere with respect to the Lebesgue measure, and the diffusion coefficient may degenerate on some subsets of the domain.
Euler's Approximations of Weak Solutions of Reflecting SDEs with Discontinuous Coefficients
We study convergence in law for the Euler and Euler-Peano schemes for stochastic differential equations reflecting on the boundary of a general convex domain. We assume that the coefficients are measurable and continuous almost everywhere with respect to the Lebesgue measure. The proofs are based on new estimates of Krylov's type for the approximations considered.
Evolutionary Pareto distributions
Exact asymptotics for boundary crossing probabilities of Brownian motion with piecewise linear trend.
Exact convergence rate for the maximum of standardized Gaussian increments.
Exact convergence rates in Erdös-Rényi type theorems for renewal processes
Exact laws for sums of ratios of order statistics from the Pareto distribution
Consider independent and identically distributed random variables {X nk, 1 ≤ k ≤ m, n ≤ 1} from the Pareto distribution. We select two order statistics from each row, X n(i) ≤ X n(j), for 1 ≤ i < j ≤ = m. Then we test to see whether or not Laws of Large Numbers with nonzero limits exist for weighted sums of the random variables R ij = X n(j)/X n(i).
Exact rate of convergence for increments of random fields.
Exact rates in Vapnik-Chervonenkis bounds