Sur l'équivalent du module de continuité des processus de diffusion
Sur un processus associé aux temps locaux browniens
Système de processus auto-stabilisants [Book]
Taux de croissance d'un subordinateur à double indice
Temps locaux d'intersection et points multiples des processus de Lévy
The average density of super-brownian motion
The Hausdorff measure of the closed support of super-brownian motion
The -Wright function in time-fractional diffusion processes: a tutorial survey.
The majorizing measure approach to sample boundedness
We describe an alternative approach to sample boundedness and continuity of stochastic processes. We show that the regularity of paths can be understood in terms of the distribution of the argument maximum. For a centered Gaussian process X(t), t ∈ T, we obtain a short proof of the exact lower bound on . Finally we prove the equivalence of the usual majorizing measure functional to its conjugate version.
The maximum of a gaussian process with nonconstant variance
The probability that brownian motion almost contains a line
Théorèmes de dérivation du type de Lebesgue et continuité presque sûre de certains processus gaussiens
Thin points for brownian motion
Topologies métrisables rendant continues les trajectoires d'un processus
Trees and asymptotic expansions for fractional stochastic differential equations
In this article, we consider an n-dimensional stochastic differential equation driven by a fractional brownian motion with Hurst parameter H>1/3. We derive an expansion for E[f(Xt)] in terms of t, where X denotes the solution to the SDE and f:ℝn→ℝ is a regular function. Comparing to F. Baudoin and L. Coutin, Stochastic Process. Appl.117 (2007) 550–574, where the same problem is studied, we provide an improvement in three different directions: we are able to consider equations with drift,...
Two results on continuity and boundedness of stochastic convolutions
Un théorème de la limite centrale dans
Une condition suffisante pour la continuité presque sûre des trajectoires de certains processus gaussiens
Une remarque sur les processus gaussiens définissant des mesures
Uniform deterministic equivalent of additive functionals and non-parametric drift estimation for one-dimensional recurrent diffusions
Usually the problem of drift estimation for a diffusion process is considered under the hypothesis of ergodicity. It is less often considered under the hypothesis of null-recurrence, simply because there are fewer limit theorems and existing ones do not apply to the whole null-recurrent class. The aim of this paper is to provide some limit theorems for additive functionals and martingales of a general (ergodic or null) recurrent diffusion which would allow us to have a somewhat unified approach...