Une simplification de l'argument de Tsirelson sur le caractère non-brownien des processus de Walsh
Une solution simple au problème de Skorokhod
Uniqueness for reflecting brownian motion in lip domains
Uniqueness of Brownian motion on Sierpiński carpets
We prove that, up to scalar multiples, there exists only one local regular Dirichlet form on a generalized Sierpi´nski carpet that is invariant with respect to the local symmetries of the carpet. Consequently, for each such fractal the law of Brownian motion is uniquely determined and the Laplacian is well defined.
Universality for conformally invariant intersection exponents
We construct a class of conformally invariant measures on sets (or paths) and we study the critical exponents called intersection exponents associated to these measures. We show that these exponents exist and that they correspond to intersection exponents between planar Brownian motions. More precisely, using the definitions and results of our paper [27], we show that any set defined under such a conformal invariant measure behaves exactly as a pack (containing maybe a non-integer number) of Brownian...
Universality of the asymptotics of the one-sided exit problem for integrated processes
We consider the one-sided exit problem – also called one-sided barrier problem – for (-fractionally) integrated random walks and Lévy processes. Our main result is that there exists a positive, non-increasing function such that the probability that any -fractionally integrated centered Lévy processes (or random walk) with some finite exponential moment stays below a fixed level until time behaves as for large . We also investigate when the fixed level can be replaced by a different barrier...
Upper and lower limits of doubly perturbed brownian motion