Brownian motion, approximation of functions, and Fourier analysis
Brownian motion, bridge excursion, and meander characterized by sampling at independent uniform times.
Brownian motion, excursions, and matrix factors
Brownian motion in a Weyl chamber, non-colliding particles, and random matrices
Brownian motion on a surface of negative curvature
Brownian motion on compact manifolds: cover time and late points.
Brownian motion on fractals and function spaces.
Brownian Motion, Reflection Groups and Tanaka Formula
Brownian particles with electrostatic repulsion on the circle : Dyson’s model for unitary random matrices revisited
The brownian motion model introduced by Dyson [7] for the eigenvalues of unitary random matrices is interpreted as a system of interacting brownian particles on the circle with electrostatic inter-particles repulsion. The aim of this paper is to define the finite particle system in a general setting including collisions between particles. Then, we study the behaviour of this system when the number of particles goes to infinity (through the empirical measure process). We prove that a limiting...
Brownian particles with electrostatic repulsion on the circle: Dyson's model for unitary random matrices revisited
The Brownian motion model introduced by Dyson [7] for the eigenvalues of unitary random matrices N x N is interpreted as a system of N interacting Brownian particles on the circle with electrostatic inter-particles repulsion. The aim of this paper is to define the finite particle system in a general setting including collisions between particles. Then, we study the behaviour of this system when the number of particles N goes to infinity (through the empirical measure process). We prove...
Brownian penalisations related to excursion lengths, VII
Limiting laws, as t→∞, for brownian motion penalised by the longest length of excursions up to t, or up to the last zero before t, or again, up to the first zero after t, are shown to exist, and are characterized.
Calcul stochastique pour les mesures signées
Cálculo diferencial estocástico para procesos con parámetro n-dimensional.
In this paper we obtain a representation of semimartingalas in the plane by means of stochastic integrals. Some applications to the study of random Markov gaussian fields are given.
Canonical decompositions of certain generalized Brownian bridges.
Central limit theorems for the brownian motion on large unitary groups
In this paper, we are concerned with the large limit of the distributions of linear combinations of the entries of a Brownian motion on the group of unitary matrices. We prove that the process of such a linear combination converges to a Gaussian one. Various scales of time and various initial distributions are considered, giving rise to various limit processes, related to the geometric construction of the unitary Brownian motion. As an application, we propose a very short proof of the asymptotic...
Changing time for two-parameter strong martingales
Chaos de Wiener et intégrale de Feynman
Chung's law of the iterated logarithm for iterated brownian motion
Coalescence of skew brownian motions
Coarsening, nucleation, and the marked brownian web