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...
Fine connectedness and alpha-excessive functions
In this article, for any Standard Process and for any , the conditions under which an -excessive function, vanishing at a point, vanishes identically are investigated.
Fluctuations of the front in a stochastic combustion model
Fonctions de corrélation des fonctions pseudo-aléatoires
Homogeneous extensions of random measures
Increasing propagation of chaos for mean field models
Inégalités pour les processus self-similaires arrêtés à un temps quelconque
Infinitely divisible processes and their potential theory. II
This second part of our two part work on i.d. process has four main goals:(1) To develop a potential operator for recurrent i.d. (infinitely divisible) processes and to use this operator to find the asymptotic behavior of the hitting distribution and Green’s function for relatively compact sets in the recurrent case.(2) To develop the appropriate notion of an equilibrium measure and Robin’s constant for Borel sets.(3) To establish the asymptotic behavior questions of a potential theoretic nature...
Infinitely divisible processes and their potential theory. I
We show that associated with every i.d. (infinitely divisible) process on a locally compact, non-compact 2nd countable Abelian group is a corresponding potential theory that yields definitive results on the behavior of the process in both space and time. Our results are general, no density or other smoothness assumptions are made on the process. In this first part of two part work we have four main goals.(1) To lay the probabilistic foundation of such processes. This mainly consists in giving the...
Interpolation of random functions.
Intersection probabilities for a chordal SLE path and a semicircle.
Intrinsic Stochastic Processes.
Julia lines of general random Dirichlet series
In this paper, we consider a random entire function defined by a random Dirichlet series where are independent and complex valued variables, . We prove that under natural conditions, for some random entire functions of order zero almost surely every horizontal line is a Julia line without an exceptional value. The result improve a theorem of J. R. Yu: Julia lines of random Dirichlet series. Bull. Sci. Math. 128 (2004), 341–353, by relaxing condition on the distribution of for such function...
Krovkin Systems of Stochastic Processes.
L'estimation du spectre de processus de droites