En marge de l'exposé de Meyer : « Géométrie différentielle stochastique »
Ensembles aléatoires, répartitions ponctuelles aléatoires, problèmes de recouvrement
Ergodic properties of marked point processes in
Erratum : “Pathwise approximations of process based on the fine structure of their filtrations”
Examples of convergence and non-convergence of Markov chains conditioned not to die.
Existence et régularité höldérienne des fonctions de bosses
We discuss the almost sure existence of random functions that can be written as sums of elementary pulses. We then estimate their uniform Hölder regularity by applying some results on coverings by random intervals.
Expected number of real zeros of Lévy and harmonizable stable random polynomials.
Explicit Karhunen-Loève expansions related to the Green function of the Laplacian
Karhunen-Loève expansions of Gaussian processes have numerous applications in Probability and Statistics. Unfortunately the set of Gaussian processes with explicitly known spectrum and eigenfunctions is narrow. An interpretation of three historical examples enables us to understand the key role of the Laplacian. This allows us to extend the set of Gaussian processes for which a very explicit Karhunen-Loève expansion can be derived.
Exponential inequalities for VLMC empirical trees
A seminal paper by Rissanen, published in 1983, introduced the class of Variable Length Markov Chains and the algorithm Context which estimates the probabilistic tree generating the chain. Even if the subject was recently considered in several papers, the central question of the rate of convergence of the algorithm remained open. This is the question we address here. We provide an exponential upper bound for the probability of incorrect estimation of the probabilistic tree, as a function...