Le semi-groupe d'une diffusion en liaison avec les trajectoires
Les -topologies en théorie du potentiel
La topologie fine a été introduite pour fournir un cadre intrinsèque à la théorie du potentiel. Cependant les ouverts fins ne possèdent pas certaines propriétés dont celle de Lindeberg. Cette considération nous conduit à introduire des topologies moins finies appelées -topologies ). Nous démontrons pour ces -topologies un critère analogue à celui établi par N. Wiener, pour les ouverts fins. Puis nous nous intéressons à la théorie des équations différentielles stochastiques sur les -ouverts.
Lévy classes and self-normalization.
Limites de quotients de fonctions harmoniques et espaces de Hardy associés à une marche aléatoire sur un groupe abélien
Limites non tangentielles, limites browniennes en probabilité et limites semi-fines.
Local admissible convergence of harmonic functions on non-homogeneous trees
We prove admissible convergence to the boundary of functions that are harmonic on a subset of a non-homogeneous tree equipped with a transition operator that satisfies uniform bounds suitable for transience. The approach is based on a discrete Green formula, suitable estimates for the Green and Poisson kernel and an analogue of the Lusin area function.
Local Fatou theorem and the density of energy on manifolds of negative curvature.
Local property of Dirichlet forms and diffusions on general state spaces.
Logarithmic capacity is not subadditive – a fine topology approach
In Landkof’s monograph [8, p. 213] it is asserted that logarithmic capacity is strongly subadditive, and therefore that it is a Choquet capacity. An example demonstrating that logarithmic capacity is not even subadditive can be found e.gi̇n [6, Example 7.20], see also [3, p. 803]. In this paper we will show this fact with the help of the fine topology in potential theory.
Lois conditionnelles des excursions markoviennes
Lois de sortie et semi-groupes basiques.
Marches de Harris sur les groupes localement compacts. II
Markov functions
Markov Processes with Identiacl Hitting Probalities.
Markov Processes with Identical Excessive Measures.
Martingales et changement de temps
Measures charging no polar sets and additive functional of Brownian motion.
Measures of finite (r,p)-energy and potentials on a separable metric space
Metastability in reversible diffusion processes I: Sharp asymptotics for capacities and exit times
We develop a potential theoretic approach to the problem of metastability for reversible diffusion processes with generators of the form on or subsets of , where is a smooth function with finitely many local minima. In analogy to previous work on discrete Markov chains, we show that metastable exit times from the attractive domains of the minima of can be related, up to multiplicative errors that tend to one as , to the capacities of suitably constructed sets. We show that these capacities...
Metastability in reversible diffusion processes II: precise asymptotics for small eigenvalues
We continue the analysis of the problem of metastability for reversible diffusion processes, initiated in [BEGK3], with a precise analysis of the low-lying spectrum of the generator. Recall that we are considering processes with generators of the form on or subsets of , where is a smooth function with finitely many local minima. Here we consider only the generic situation where the depths of all local minima are different. We show that in general the exponentially small part of the spectrum...