Branching and interacting particle systems. Approximations of Feynman-Kac formulae with applications to non-linear filtering
Branching processes, and random-cluster measures on trees
Random-cluster measures on infinite regular trees are studied in conjunction with a general type of ‘boundary condition’, namely an equivalence relation on the set of infinite paths of the tree. The uniqueness and non-uniqueness of random-cluster measures are explored for certain classes of equivalence relations. In proving uniqueness, the following problem concerning branching processes is encountered and answered. Consider bond percolation on the family-tree of a branching process. What is the...
Branching processes, random trees and superprocesses.
Branching random walk with catalysts.
Breakdown processes of systems in parallel
Breakdown time distributions of systems in series
Brèves communications. Une démonstration directe de la formule de Pollaczek-Khintchine
Brownian dynamics of globules.
Brownian local times.
Brownian motion and parabolic Anderson model in a renormalized Poisson potential
A method known as renormalization is proposed for constructing some more physically realistic random potentials in a Poisson cloud. The Brownian motion in the renormalized random potential and related parabolic Anderson models are modeled. With the renormalization, for example, the models consistent to Newton’s law of universal attraction can be rigorously constructed.
Brownian motion and random obstacles.
Brownian motion in a Poisson obstacle field
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...
Bulk input queues with quorum and multiple vacations.
Busy period analysis, rare events and transient behavior in fluid flow models.
Busy period problems in the GI/G/∞ queue