Eigenvalue expansions for Brownian motion with an application to occupation times.
Entrelacements de semi-groupes provenant de paires de Gelfand
On donne des exemples d'entrelacements entre semi-groupes markoviens obtenus au moyen de considérations de théorie des groupes sur les paires de Gelfand
Entrelacements de semi-groupes provenant de paires de Gelfand
On donne des exemples d'entrelacements entre semi-groupes markoviens obtenus au moyen de considérations de théorie des groupes sur les paires de Gelfand
Ergodic behaviour of stochastic parabolic equations
The ergodic behaviour of homogeneous strong Feller irreducible Markov processes in Banach spaces is studied; in particular, existence and uniqueness of finite and -finite invariant measures are considered. The results obtained are applied to solutions of stochastic parabolic equations.
Ergodic properties of an operator obtained from a continuous representation
Ergodic properties of multidimensional Brownian motion with rebirth.
Erneuerungssätze für Prozesse mit stationären unabhängigen Zuwächsen.
Erratum Invariant measures for Markov processes arising from iterated function systems with place-dependent probabilities
Estimates of the potential kernel and Harnack's inequality for the anisotropic fractional Laplacian
We characterize those homogeneous translation invariant symmetric non-local operators with positive maximum principle whose harmonic functions satisfy Harnack's inequality. We also estimate the corresponding semigroup and the potential kernel.
Explicit parametrix and local limit theorems for some degenerate diffusion processes
For a class of degenerate diffusion processes of rank 2, i.e. when only Poisson brackets of order one are needed to span the whole space, we obtain a parametrix representation of McKean–Singer [J. Differential Geom.1 (1967) 43–69] type for the density. We therefrom derive an explicit gaussian upper bound and a partial lower bound that characterize the additional singularity induced by the degeneracy. This particular representation then allows to give a local limit theorem with the usual convergence...