Estimates of the Hausdorff dimension of the boundary of positive brownian sheet components
Estimator of variance of Wiener process based on its integral
Étude asymptotique du temps passé par le mouvement brownien dans un cône
Étude de certains processus (stochastiquement) différentiables ou holomorphes
Étude des extrêmes d'une suite stationnaire m-dépendante avec une application relative aux accroissements du processus de Wiener
Étude probabiliste de l'opérateur de Schrödinger
Exact asymptotics for boundary crossing probabilities of Brownian motion with piecewise linear trend.
Exact rates of convergence to the local times of symmetric Lévy processes
Excursion laws and exceptional points on brownian paths
Excursions of the integral of the brownian motion
The integrated brownian motion is sometimes known as the Langevin process. Lachal studied several excursion laws induced by the latter. Here we follow a different point of view developed by Pitman for general stationary processes. We first construct a stationary Langevin process and then determine explicitly its stationary excursion measure. This is then used to provide new descriptions of Itô’s excursion measure of the Langevin process reflected at a completely inelastic boundary, which has been...
Existence and asymptotic behaviour of some time-inhomogeneous diffusions
Let us consider a solution of a one-dimensional stochastic differential equation driven by a standard Brownian motion with time-inhomogeneous drift coefficient . This process can be viewed as a Brownian motion evolving in a potential, possibly singular, depending on time. We prove results on the existence and uniqueness of solution, study its asymptotic behaviour and made a precise description, in terms of parameters , and , of the recurrence, transience and convergence. More precisely, asymptotic...
Existence of small oscillations at zeros of brownian motion
Exponential functionals of brownian motion and class-one Whittaker functions
We consider exponential functionals of a brownian motion with drift in ℝn, defined via a collection of linear functionals. We give a characterisation of the Laplace transform of their joint law as the unique bounded solution, up to a constant factor, to a Schrödinger-type partial differential equation. We derive a similar equation for the probability density. We then characterise all diffusions which can be interpreted as having the law of the brownian motion with drift conditioned on the law of...
Exponential functionals of Brownian motion. I: Probability laws at fixed time.
Exponential functionals of Brownian motion. II: Some related diffusion processes.
Exponential moments for the renormalized self-intersection local time of planar brownian motion
Exponential rate of convergence of maximum likelihood estimators for inhomogeneous Wiener processes
Exposants critiques pour le mouvement brownien et les marches aléatoires
Extending Lévy's characterisation of brownian motion
Extending the Wong-Zakai theorem to reversible Markov processes
We show how to construct a canonical choice of stochastic area for paths of reversible Markov processes satisfying a weak Hölder condition, and hence demonstrate that the sample paths of such processes are rough paths in the sense of Lyons. We further prove that certain polygonal approximations to these paths and their areas converge in -variation norm. As a corollary of this result and standard properties of rough paths, we are able to provide a significant generalization of the classical result...