This paper is devoted to analyze several properties of the bifractional Brownian motion introduced by Houdré and Villa. This process is a self-similar Gaussian process depending on two parameters H and K and it constitutes a natural generalization of the fractional Brownian motion (which is obtained for K = 1). We adopt the strategy of the stochastic calculus via regularization. Particular inte...

We introduce the fractional mixed fractional Brownian sheet and investigate the small ball behavior of its sup-norm statistic by establishing a general result on the small ball probability of the sum of two not necessarily independent joint Gaussian random vectors. Then, we state general conditions and characterize the sufficiency part of the lower classes of some statistics of the above proces...

We call a point process Z on R exp-1-stable if for every α, β ∈ R with e + e = 1, Z is equal in law to TαZ + TβZ , where Z ′ is an independent copy of Z and Tx is the translation by x. Such processes appear in the study of the extremal particles of branching Brownian motion and branching random walk and several authors have proven in that setting the existence of a point process D on R such tha...

Abstract. We consider the number of nodes in the levels of unlabelled rooted random trees and show that the stochastic process given by the properly scaled level sizes weakly converges to the local time of a standard Brownian excursion. Furthermore we compute the average and the distribution of the height of such trees. These results extend existing results for conditioned Galton-Watson trees a...

In this paper we study one-dimensional reflected backward stochastic differential equation when the noise is driven by a Brownian motion and an independent Poisson point process when the solution is forced to stay above a right continuous left-hand limited obstacle. We prove existence and uniqueness of the solution by using a penalization method combined with a monotonic limit theorem.

Abstract. We consider a super-Brownian motion X. Its canonical measures can be studied through the path-valued process called the Brownian snake. We obtain the limiting behavior of the volume of the ε-neighborhood for the range of the Brownian snake, and as a consequence we derive the analogous result for the range of super-Brownian motion and for the support of the integrated super-Brownian ex...

"This paper is devoted to the study of a convex stochastic sweeping process with fractional Brownian by time delay. The approach based on dis- cretizing functional differential inclusions."

The question of the equivalence in law of Gaussian processes has been widely studied in the sixties-seventies.(5,6,9,14) Recently, the problem has been reopened by several authors, due to the intensive study of the fractional Brownian and of stochastic calculus with respect to this process. Precisely, the Wiener integral representation of the fractional Brownian motion with respect to the Brown...