Large deviations for multiple Wiener-Itô integral processes
Laws of the iterated logarithm for the brownian snake
Le théorème de convergence des martingales dans les variétés riemanniennes d'après R.W. Darling et W.A. Zheng
Level sets of multiparameter Brownian motions.
Level sets of random fields and applications: specular points and wave crests.
Levels at which every brownian excursion is exceptional
Lévy processes that can creep downwards never increase
Limsup random fractals.
Local Asymptotic Normality Property for Lacunar Wavelet Series multifractal model
We consider a lacunar wavelet series function observed with an additive Brownian motion. Such functions are statistically characterized by two parameters. The first parameter governs the lacunarity of the wavelet coefficients while the second one governs its intensity. In this paper, we establish the local and asymptotic normality (LAN) of the model, with respect to this couple of parameters. This enables to prove the optimality of an estimator for the lacunarity parameter, and to build optimal...
Local Asymptotic Normality Property for Lacunar Wavelet Series multifractal model*
We consider a lacunar wavelet series function observed with an additive Brownian motion. Such functions are statistically characterized by two parameters. The first parameter governs the lacunarity of the wavelet coefficients while the second one governs its intensity. In this paper, we establish the local and asymptotic normality (LAN) of the model, with respect to this couple of parameters. This enables to prove the optimality of an estimator for the lacunarity parameter, and to build optimal...
Local nondeterminism and local times of general stochastic processes
Local property of Dirichlet forms and diffusions on general state spaces.
Local time and related sample paths of filtered white noises
We study the existence and the regularity of the local time of filtered white noises . We will also give Chung’s form of the law of iterated logarithm for , this shows that the result on the Hölder regularity, with respect to time, of the local time is sharp.
Loop-free Markov chains as determinantal point processes
We show that any loop-free Markov chain on a discrete space can be viewed as a determinantal point process. As an application, we prove central limit theorems for the number of particles in a window for renewal processes and Markov renewal processes with Bernoulli noise.
Majorizing Measures and Ultrametric Spaces
Talagrand's proof of the sufficiency of existence of a majorizing measure for the sample boundedness of processes with bounded increments used a contraction from a certain ultrametric space. We give a short proof of existence of such an ultrametric using admissible sequences of nets.
Markov chain intersections and the loop-erased walk
Markov processes and convex minorants
Measurability of stochastic process and approximate continuity of its correlation function.
Mesure de Hausdorff de la trajectoire de certains processus à accroissements indépendants et stationnaires
Mild solution of the heat equation with a general stochastic measure
The stochastic heat equation on [0,T]×ℝ driven by a general stochastic measure is investigated. Existence and uniqueness of the solution is established. Hölder regularity of the solution in time and space variables is proved.