Potential theory for a family of several Markov processes
Potential theory of one-dimensional geometric stable processes
The purpose of this paper is to find optimal estimates for the Green function and the Poisson kernel for a half-line and intervals of the geometric stable process with parameter α ∈ (0,2]. This process has an infinitesimal generator of the form . As an application we prove the global scale invariant Harnack inequality as well as the boundary Harnack principle.
Potentials of a Markov process are expected suprema
Expected suprema of a function f observed along the paths of a nice Markov process define an excessive function, and in fact a potential if f vanishes at the boundary. Conversely, we show under mild regularity conditions that any potential admits a representation in terms of expected suprema. Moreover, we identify the maximal and the minimal representing function in terms of probabilistic potential theory. Our results are motivated by the work of El Karoui and Meziou (2006) on the max-plus decomposition...
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.
Potentialtheorie auf dem Sierpinski gasket.
Potentiel markovien récurrent des chaînes de Harris
Nous montrons que toute probabilité de transition sur un espace mesurable correspondant à une chaîne de Markov vérifiant la condition de récurrence de Harris, admet au moins un opérateur potentiel positif ; à partir de là, nous développons une théorie du “potentiel logarithmique” pour ces probabilités de transition, en étudiant notamment de manière approfondie un cône de fonctions dites spéciales.
Potentiels de fonctionnelles additives. Un contre-exemple de Knight
Potentiels de Green et fonctionnelles additives
Probabilistic Approach to the Neumann Problem for a Symmetric Operator
2000 Mathematics Subject Classification: Primary 60J45, 60J50, 35Cxx; Secondary 31Cxx.We give a probabilistic formula for the solution of a non-homogeneous Neumann problem for a symmetric nondegenerate operator of second order in a bounded domain. We begin with a g-Hölder matrix and a C^1,g domain, g > 0, and then consider extensions. The solutions are expressed as a double layer potential instead of a single layer potential; in particular a new boundary function is discovered and boundary random...
Processus de Ray et théorie du balayage.
Processus stationnaires et mesures de Palm du flot spécial sous une fonction
Propriétés d'invariance du domaine du générateur infinitésimal étendu d'un processus de Markov
Quand l'inégalité log-Sobolev implique l'inégalité de trou spectral
Quelques inégalités concernant les martingales
Quelques remarques sur un article de Donsker et Varadhan
Random walk on graphs with regular resistance and volume growth
In this paper characterizations of graphs satisfying heat kernel estimates for a wide class of space–time scaling functions are given. The equivalence of the two-sided heat kernel estimate and the parabolic Harnack inequality is also shown via the equivalence of the upper (lower) heat kernel estimate to the parabolic mean value (and super mean value) inequality.
Random walk on periodic trees.
Ray Processes on Locally Compact Spaces.
Recouvrements aléatoires et théorie du potentiel
Recurrence and transience for long-range reversible random walks on a random point process.