Remarques sur certaines constructions des mouvements browniens fractionnaires
Remarques sur le processus d'Ornstein-Uhlenbeck en dimension infinie
Remarques sur une formule de Paul Lévy
Renewal property of the extrema and tree property of the excursion of a one-dimensional brownian motion
Renormalisation et convergence en loi pour certaines intégrales multiples associées au mouvement brownien dans
Renormalisation et convergence en loi pour les temps locaux d’intersection du mouvement brownien dans
Representación de variables en el movimiento browniano con deriva.
Se estudia la representación de variables positivas en un movimiento browniano con deriva, mediante tiempos de espera minimales asociados a barreras. Se trata también la representación de procesos crecientes, discretos y continuos por la derecha.
Représentation des endomorphismes de l'espace de Wiener qui préservent les martingales
Representation formula for the entropy and functional inequalities
We prove a stochastic formula for the Gaussian relative entropy in the spirit of Borell’s formula for the Laplace transform. As an application, we give simple proofs of a number of functional inequalities.
Restricted mean value property for positive functions.
Résultats récents de A. Benveniste en théorie des flots
Revisiting the sample path of Brownian motion
Brownian motion is the most studied of all stochastic processes; it is also the basis for stochastic analysis developed in the second half of the 20th century. The fine properties of the sample path of a Brownian motion have been carefully studied, starting with the fundamental work of Paul Lévy who also considered more general processes with independent increments and extended the Brownian motion results to this class. Lévy showed that a Brownian path in d (d ≥ 2) dimensions had zero Lebesgue measure;...
Rolling with “slipping” : I
Semigroups associated with generalized Brownian functional.
Semimartingale decomposition of convex functions of continuous semimartingales by brownian perturbation
In this note we prove that the local martingale part of a convex function f of a d-dimensional semimartingale X = M + A can be written in terms of an Itô stochastic integral ∫H(X)dM, where H(x) is some particular measurable choice of subgradient ∇ f ( x ) off at x, and M is the martingale part of X. This result was first proved by Bouleau in [N. Bouleau, C. R. Acad. Sci. Paris Sér. I Math. 292 (1981) 87–90]. Here we present a new treatment of the problem. We first prove the result for x10ff65;...
Séries de variables aléatoires gaussiennes à valeurs dans . Application aux produits d’espaces de Wiener abstraits
Sharp estimates of the Green function of hyperbolic Brownian motion
The main objective of the work is to provide sharp two-sided estimates of the λ-Green function, λ ≥ 0, of the hyperbolic Brownian motion of a half-space. We rely on the recent results obtained by K. Bogus and J. Małecki (2015), regarding precise estimates of the Bessel heat kernel for half-lines. We also substantially use the results of H. Matsumoto and M. Yor (2005) on distributions of exponential functionals of Brownian motion.
Sharp small ball asymptotics for Slepian and Watson processes in Hilbert norm.
Shortest excursion lengths
Simple examples of non-generating Girsanov processes