Sur une inégalité de Sobolev logarithmique pour une diffusion unidimensionnelle
Symmetric reflected diffusions
Symmetries of Excessive Measures of Markov Processes.
Systèmes de Lévy des processus de Markov.
Temps locaux d'intersection et points multiples des processus de Lévy
Temps locaux et l'intégrale d'aire de Lusin
The Brownian fractional motion as a limit of some types of stochastic processes.
The density of the area integral in
Let be a harmonic function in the half-plane , . We define a family of functionals , that are analogs of the family of local times associated to the process where is Brownian motion in . We show that is bounded in if and only if belongs to , an equivalence already proved by Barlow and Yor for the supremum of the local times. Our proof relies on the theory of singular integrals due to Caldéron and Zygmund, rather than the stochastic calculus.
The energy functional, balayage, and capacity
The excessive domination principle is equivalent to the weak sector condition
The existence of the potential operator associated with an equicontinuous semigroup of class
The Harmonic Functions of Mean Ergodic Markov Semigroups.
The Harmonie Space Associated with a "Reasonable" Standard Process.
The lifetime of conditional brownian motion in the plane
The logarithmic Sobolev constant of some finite Markov chains
The logarithmic Sobolev constant is always bounded above by half the spectral gap. It is natural to ask when this inequality is an equality. We consider this question in the context of reversible Markov chains on small finite state spaces. In particular, we prove that equality holds for simple random walk on the five cycle and we discuss assorted families of chains on three and four points.
The Martin entrance boundary of the Galton–Watson process
The Max-Plus Martin boundary.
The Probabilistic Solution of the Dirichlet Problem for Degenerate Elliptic Equations
We study the Dirichlet problem for degenerate elliptic equations, and show that the probabilistic solution is a unique viscosity solution.
The quasi-sure ratio ergodic theorem
The Skorokhod embedding problem and its offspring.