Small tails for the supremum of a gaussian process
Small-time behaviour of Lévy processes.
Smoothness of Itô maps and diffusion processes on path spaces (I)
Some applications of subordinators to local times of Markov processes.
Some limit theorems for local time
Some results on stochastic convolutions arising in Volterra equations perturbed by noise
Regularity of stochastic convolutions corresponding to a Volterra equation, perturbed by a white noise, is studied. Under suitable assumptions, hölderianity of the corresponding trajectories is proved.
Some results on the continuity of stable processes and the domain of attraction of continuous stable processes
Some thoughts about Segal's ergodic theorem
Over fifty years ago, Irving Segal proved a theorem which leads to a characterization of those orthogonal transformations on a Hilbert space which induce ergodic transformations. Because Segal did not present his result in a way which made it readily accessible to specialists in ergodic theory, it was difficult for them to appreciate what he had done. The purpose of this note is to state and prove Segal's result in a way which, I hope, will win it the recognition which it deserves.
Stochastic continuity and approximation
This work is concerned with the study of stochastic processes which are continuous in probability, over various parameter spaces, from the point of view of approximation and extension. A stochastic version of the classical theorem of Mergelyan on polynomial approximation is shown to be valid for subsets of the plane whose boundaries are sets of rational approximation. In a similar vein, one can obtain a version in the context of continuity in probability of the theorem of Arakelyan on the uniform...
Strict concavity of the intersection exponent for Brownian motion in two and three dimensions.
Sublineare Abbildungen und ein Konvergenzsatz von Banach.
Sufficient conditions for the continuity of stationary gaussian processes and applications to random series of functions
Let be a stochastically continuous, separable, Gaussian process with . A sufficient condition, in terms of the monotone rearrangement of , is obtained for to have continuous sample paths almost surely. This result is applied to a wide class of random series of functions, in particular, to random Fourier series.
Sur la convergence des semimartingales continues dans et des martingales dans une variété
Sur la loi du maximum de certains processus gaussions sur le tore
Sur la mesure de Hausdorff de la courbe brownienne
Sur la -variation des surmartingales
Sur la propriété de la limite centrale dans
Sur la régularité de certaines fonctions aléatoires d'Ornstein-Uhlenbeck
Sur le premier instant de passage de l'intégrale du mouvement brownien
Sur le temps local d'intersection du mouvement brownien plan et la méthode de renormalisation de Varadhan