On some regularity properties of solutions to stochastic evolution equations in Hilbert spaces
On some sample path properties of Skorohod integral processes
On subsets of and -stable processes
On suprema of Lévy processes and application in risk theory
Let X̂=C−Y where Y is a general one-dimensional Lévy process and C an independent subordinator. Consider the times when a new supremum of X̂ is reached by a jump of the subordinator C. We give a necessary and sufficient condition in order for such times to be discrete. When this is the case and X̂ drifts to −∞, we decompose the absolute supremum of X̂ at these times, and derive a Pollaczek–Hinchin-type formula for the distribution function of the supremum.
On Talagrand's Admissible Net Approach to Majorizing Measures and Boundedness of Stochastic Processes
We show that the main result of [1] on sufficiency of existence of a majorizing measure for boundedness of a stochastic process can be naturally split in two theorems, each of independent interest. The first is that the existence of a majorizing measure is sufficient for the existence of a sequence of admissible nets (as recently introduced by Talagrand [5]), and the second that the existence of a sequence of admissible nets is sufficient for sample boundedness of a stochastic process with bounded...
On the approximate solutions of the Stratonovitch equation.
On the boundedness of Bernoulli processes over thin sets.
On the explosion of the local times along lines of brownian sheet
On the exponentials of fractional Ornstein-Uhlenbeck processes.
On the local time of sub-fractional Brownian motion
be a sub-fractional Brownian motion with . We establish the existence, the joint continuity and the Hölder regularity of the local time of . We will also give Chung’s form of the law of iterated logarithm for . This results are obtained with the decomposition of the sub-fractional Brownian motion into the sum of fractional Brownian motion plus a stochastic process with absolutely continuous trajectories. This decomposition is given by Ruiz de Chavez and Tudor [10].
On the mixed fractional Brownian motion.
On the rate of growth of Lev́y processes with no positive jumps conditioned to stay positive.
On the sample path behavior of the first passage time process of a brownian motion with drift
On the sample paths of diagonal brownian motions on the infinite dimensional torus
On the time of the maximum of Brownian motion with drift.
On trajectories of Gaussian Markov random fields
Oscillations de fonctions aléatoires gaussiennes à valeurs vectorielles.
Path continuity and last exit distributions
Path properties of a class of locally asymptotically self similar processes.
Pénalisations de l’araignée brownienne
Dans cet article, nous pénalisons la loi d’une araignée brownienne prenant ses valeurs dans un ensemble fini de demi-droites concourantes, avec un poids égal à , où est un réel positif, une famille de réels indexés par , un paramètre réel, la distance de à l’origine, () la demi-droite sur laquelle se trouve , le temps local de à l’origine, et la constante de normalisation. Nous montrons que la famille des mesures de probabilité obtenue par ces pénalisations converge vers...