Brownian motion, bridge excursion, and meander characterized by sampling at independent uniform times.
Brownian motion, excursions, and matrix factors
Brownian motion in a Poisson obstacle field
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 motion with respect to time-changing riemannian metrics, applications to Ricci flow
We generalize brownian motion on a riemannian manifold to the case of a family of metrics which depends on time. Such questions are natural for equations like the heat equation with respect to time dependent laplacians (inhomogeneous diffusions). In this paper we are in particular interested in the Ricci flow which provides an intrinsic family of time dependent metrics. We give a notion of parallel transport along this brownian motion, and establish a generalization of the Dohrn–Guerra or damped...
Brownian motions in the diffeomorphism group I
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.
Brownian representations of cylindrical local martingales, martingale problem and strong Markov property of weak solutions of SPDEs in Banach spaces
The paper deals with three issues. First we show a sufficient condition for a cylindrical local martingale to be a stochastic integral with respect to a cylindrical Wiener process. Secondly, we state an infinite dimensional version of the martingale problem of Stroock and Varadhan, and finally we apply the results to show that a weak existence plus uniqueness in law for deterministic initial conditions for an abstract stochastic evolution equation in a Banach space implies the strong Markov property....
BSDE associated with Lévy processes and application to PDIE.
BSDEs with polynomial growth generators.
BSDEs with random terminal time and semilinear elliptic PDEs in divergence form
We study connections between Sobolev space solutions of the Dirichlet problem for semilinear second order elliptic equations in divergence form and solutions of backward stochastic differential equations with random terminal time.
BSDEs with two reflecting barriers driven by a Brownian and a Poisson noise and related Dynkin game.
Bulk input queues with quorum and multiple vacations.
Burkholder's inequality for multiindex martingales.