Un modèle de champ moyen, nucléation et bifurcation
Un nouveau principe de grandes déviations en théorie du filtrage non linéaire
Un théorème de Schilder pour des fonctionnelles browniennes non régulières
Une inégalité de Bennett pour les maxima de processus empiriques
Une remarque sur la théorie des grandes déviations
Une transformation de Cramer sur le dual de
Uniform deterministic equivalent of additive functionals and non-parametric drift estimation for one-dimensional recurrent diffusions
Usually the problem of drift estimation for a diffusion process is considered under the hypothesis of ergodicity. It is less often considered under the hypothesis of null-recurrence, simply because there are fewer limit theorems and existing ones do not apply to the whole null-recurrent class. The aim of this paper is to provide some limit theorems for additive functionals and martingales of a general (ergodic or null) recurrent diffusion which would allow us to have a somewhat unified approach...
Uniform exponential bound for the normalized empirical process
Upper large deviations for maximal flows through a tilted cylinder
We consider the standard first passage percolation model in ℤd for d ≥ 2 and we study the maximal flow from the upper half part to the lower half part (respectively from the top to the bottom) of a cylinder whose basis is a hyperrectangle of sidelength proportional to n and whose height is h(n) for a certain height function h. We denote this maximal flow by τn (respectively φn). We emphasize the fact that the cylinder may be tilted. We look at the probability that these flows, rescaled by the surface...
Upper tails of self-intersection local times of random walks: survey of proof techniques
The asymptotics of the probability that the self-intersection local time of a random walk on exceeds its expectation by a large amount is a fascinating subject because of its relation to some models from Statistical Mechanics, to large-deviation theory and variational analysis and because of the variety of the effects that can be observed. However, the proof of the upper bound is notoriously difficult and requires various sophisticated techniques. We survey some heuristics and some recently elaborated...