Perturbation des résolvantes et des semi-groupes par une mesure de Radon positive.
Poincaré inequalities and hitting times
Equivalence of the spectral gap, exponential integrability of hitting times and Lyapunov conditions is well known. We give here the correspondence (with quantitative results) for reversible diffusion processes. As a consequence, we generalize results of Bobkov in the one dimensional case on the value of the Poincaré constant for log-concave measures to superlinear potentials. Finally, we study various functional inequalities under different hitting times integrability conditions (polynomial,…)....
Poincaré inequality for some measures in Hilbert spaces and application to spectral gap for transition semigroups
Potential-theoretical methods in the construction of measure-valued Markov branching processes
We develop potential-theoretical methods in the construction of measure-valued branching processes.We complete results of P. J. Fitzsimmons and E. B. Dynkin on the construction, regularity and other properties of the superprocess associated with a given right process and a branching mechanism.
Precise estimates on the rate at which certain diffusions tend to equilibrium.
Propriétés d'invariance du domaine du générateur infinitésimal étendu d'un processus de Markov
Pseudo differential operators with negative definite symbols of variable order.
One way to represent the generator of a Markov process is given by pseudo differential operators. Above all this is due to the fact that the generator satisfies the so-called positive maximum principle (...).