Let (Bt; t â‰¥ 0) be a onedimensional Brownian motion, with local time process (Lt ; t â‰¥ 0, x âˆˆ R). We determine the rate of decay of Z t (x) := Ex [

â€¢ In Section 1, we present a number of classical results concerningthe GeneralizedGamma Convolution ( : GGC) variables, their Wiener-Gamma representations, and relation with the Dirichlet processes.â€¦ (More)

With the help of two Skorokhod embeddings, we construct martingales which enjoy the Brownian scaling property and the (inhomogeneous) Markov property. The second method necessitates randomization,â€¦ (More)

Results of penalization of a one-dimensional Brownian motion (Xt), by its one-sided maximum (St = sup 0â‰¤uâ‰¤t Xu), which were recently obtained by the authors are improved with the consideration-in theâ€¦ (More)

We describe the limit laws, as t â†’ âˆž, of a Bessel process (Rs, s â‰¤ t) of dimension d âˆˆ (0, 2) penalized by an integrable function of its local time Lt at 0, thus extending our previous work of thisâ€¦ (More)

We show that Pitmanâ€™s theorem relating Brownian motion and the BES(3) process, as well as the Ray-Knight theorems for Brownian local times remain valid, mutatis mutandis, under the limiting laws ofâ€¦ (More)

Consider {XÎµ t : t â‰¥ 0} (Îµ > 0), the solution starting from 0 of a stochastic differential equation, which is a small Brownian perturbation of the one-dimensional ordinary differential equation xt =â€¦ (More)

We develop a Brownian penalisation procedure related to weight processes (Ft) of the type : Ft := f(It, St) where f is a bounded function with compact support and St (resp. It) is the one-sidedâ€¦ (More)