Sur un Ensemble de lois de Probabilite Associees a la loi Normale
Sur un résultat de P. Revesz et un résultat de A. Renyi
Sur un type de convergence intermédiaire entre la convergence en loi et la convergence en probabilité
Sur une classe des fonctionnelles des processus stables et des marches aléatoires
Sur une conjecture de L. E. Dubins
Symmetric and centered binomial approximation of sums of locally dependent random variables.
Systèmes de particules et mesures-martingales : un théorème de propagation du chaos
Tail approximations for samples from a finite population with applications to permutation tests
This paper derives an explicit approximation for the tail probability of a sum of sample values taken without replacement from an unrestricted finite population. The approximation is shown to hold under no conditions in a wide range with relative error given in terms of the standardized absolute third moment of the population, β3N. This approximation is used to obtain a result comparable to the well-known Cramér large deviation result in the independent case, but with no restrictions on the sampled...
Tail approximations for samples from a finite population with applications to permutation tests
This paper derives an explicit approximation for the tail probability of a sum of sample values taken without replacement from an unrestricted finite population. The approximation is shown to hold under no conditions in a wide range with relative error given in terms of the standardized absolute third moment of the population, β3N. This approximation is used to obtain a result comparable to the well-known Cramér large deviation result in the independent ...
Tessellations of random maps of arbitrary genus
We investigate Voronoi-like tessellations of bipartite quadrangulations on surfaces of arbitrary genus, by using a natural generalization of a bijection of Marcus and Schaeffer allowing one to encode such structures by labeled maps with a fixed number of faces. We investigate the scaling limits of the latter. Applications include asymptotic enumeration results for quadrangulations, and typical metric properties of randomly sampled quadrangulations. In particular, we show that scaling limits of these...
Testing randomness of spatial point patterns with the Ripley statistic
Aggregation patterns are often visually detected in sets of location data. These clusters may be the result of interesting dynamics or the effect of pure randomness. We build an asymptotically Gaussian test for the hypothesis of randomness corresponding to a homogeneous Poisson point process. We first compute the exact first and second moment of the Ripley K-statistic under the homogeneous Poisson point process model. Then we prove the asymptotic normality of a vector of such statistics for different...
Tests for the presence of trends in linear processes [Book]
The almost sure central limit theorems for certain order statistics of some stationary Gaussian sequences
Suppose that X1, X2, … is some stationary zero mean Gaussian sequence with unit variance. Let {kn} be a certain nondecreasing sequence of positive integers, [...] denote the kn largest maximum of X1, … Xn. We aim at proving the almost sure central limit theorems for the suitably normalized sequence [...] under certain additional assumptions on {kn} and the covariance function [...]
The Arcsine law as the limit of the internal DLA cluster generated by Sinai’s walk
We identify the limit of the internal DLA cluster generated by Sinai’s walk as the law of a functional of a brownian motion which turns out to be a new interpretation of the Arcsine law.
The asymptotic distribution of the bootstrap sample mean of an infinitesimal array
The asymptotics of spherical functions and the central limit theorem on symmetric cones
We prove a central limit theorem for certain invariant random variables on the symmetric cone in a formally real Jordan algebra. This extends form the previous results of Richards and Terras on the cone of real positive definite matrices.
The Berry-Esseen theorem for rank statistics
The best constant in the Khintchine inequality for complex Steinhaus variables, the case p=1
The bootstrap of the mean with arbitrary bootstrap sample size
The Brownian fractional motion as a limit of some types of stochastic processes.