Let M=(Mt)t=0 be any continuous real-valued stochastic process. We prove that if there exists a sequence (an)n=1 of real numbers which converges to 0 and such that M satisfies the reflection property at all levels an and 2an with n=1, then M is an Ocone local martingale with respect to its...

We consider some special classes of Lévy processes with no gaussian component whose Lévy measure is of the type , where [nu] is the density of the stable Lévy measure and [gamma] is a positive parameter which depends on its characteristics. These processes were introduced in [M. E. Caballero,...

In the present paper we compute the laws of some functionals of doubly perturbed Brownian motion, which is the solution of the equation Xt=Bt+[alpha] sups[less-than-or-equals, slant]t Xs+[beta] infs[less-than-or-equals, slant]t Xs, where [alpha],[beta]1, and B is a real Brownian motion. We first...

We first give an interpretation for the conditioning to stay positive (respectively, to die at 0) for a large class of Lévy processes starting at x 0. Next, we specify the laws of the pre-minimum and post-minimum parts of a Lévy process conditioned to stay positive. We show that, these parts...