Représentation d’un semigroupe d’opérateurs sur un espace par des noyaux. Remarques sur deux articles de S.E. Kuznetsov
Representation formula for the entropy and functional inequalities
We prove a stochastic formula for the Gaussian relative entropy in the spirit of Borell’s formula for the Laplace transform. As an application, we give simple proofs of a number of functional inequalities.
Representations of excessive functions.
Resonance and anti-resonance in the design of chemotherapeutic protocols.
Restricted exchangeable partitions and embedding of associated hierarchies in continuum random trees
We introduce the notion of a restricted exchangeable partition of . We obtain integral representations, consider associated fragmentations, embeddings into continuum random trees and convergence to such limit trees. In particular, we deduce from the general theory developed here a limit result conjectured previously for Ford’s alpha model and its extension, the alpha-gamma model, where restricted exchangeability arises naturally.
Restricted mean value property for positive functions.
Restrictions of CP-semigroups to maximal commutative subalgebras
We give a necessary and sufficient criterion for a normal CP-map on a von Neumann algebra to admit a restriction to a maximal commutative subalgebra. We apply this result to give a far reaching generalization of Rebolledo's sufficient criterion for the Lindblad generator of a Markov semigroup on ℬ(G).
Résultats d'Atkinson sur les processus de Markov
Résultats récents de A. Benveniste en théorie des flots
Résultats sur l'irréductibilité et la conservativité de la chaîne de différences absolues
Retour aux retournements
Retour sur la théorie de Littlewood-Paley
Return probabilities of a simple random walk on percolation clusters.
Reversibility for diffusions via quasi-invarience
Reversible distributions of multi-allelic Gillespie–Sato diffusion models
Revisiting the sample path of Brownian motion
Brownian motion is the most studied of all stochastic processes; it is also the basis for stochastic analysis developed in the second half of the 20th century. The fine properties of the sample path of a Brownian motion have been carefully studied, starting with the fundamental work of Paul Lévy who also considered more general processes with independent increments and extended the Brownian motion results to this class. Lévy showed that a Brownian path in d (d ≥ 2) dimensions had zero Lebesgue measure;...
Revuz Measures and Time Changes.
Riccati's differential equation in birth-death processes.
This note reviews the occurrence of Riccati's equation in three birth-death type processes, and outlines their solutions.
Riesz potentials derived by one-mode interacting Fock space approach
The main aim of this short paper is to study Riesz potentials on one-mode interacting Fock spaces equipped with deformed annihilation, creation, and neutral operators with constants and , as in equations (1.4)-(1.6). First, to emphasize the importance of these constants, we summarize our previous results on the Hilbert space of analytic L² functions with respect to a probability measure on ℂ. Then we consider the Riesz kernels of order 2α, , on ℂ if , which can be derived from the Bessel...
Riesz representation and duality of Markov processes