-harmonic measure is not additive on null sets
When and the -harmonic measure on the boundary of the half plane is not additive on null sets. In fact, there are finitely many sets , ,..., in , of -harmonic measure zero, such that .
-variation de fonctions aléatoires. 1ère partie : séries de Rademacher
-variation de fonctions aléatoires. 2ième partie : processus à accroissements indépendants
Palm theory for random time changes.
Parabolic Harnack inequality and estimates of Markov chains on graphs.
On a graph, we give a characterization of a parabolic Harnack inequality and Gaussian estimates for reversible Markov chains by geometric properties (volume regularity and Poincaré inequality).
Parabolic Harnack inequality and local limit theorem for percolation clusters.
Parada óptima con horizonte aleatorio.
Analizamos el problema de parada óptima con horizonte aleatorio en procesos de Markov con tiempo continuo. En concreto, estudiamos el caso en el que el horizonte es el tiempo de primera entrada en el interior de un cerrado B. Definimos las funciones B-excesivas y vemos su relación con el pago del problema de parada óptima. Posteriormente introducimos varios conjuntos, que aparecen de forma natural en el problema y que nos permiten caracterizar los dominios de parada. Por último consideramos el caso...
Parametrization and geometric analysis of coordination controllers for multi-agent systems
In this paper, we address distributed control structures for multi-agent systems with linear controlled agent dynamics. We consider the parametrization and related geometric structures of the coordination controllers for multi-agent systems with fixed topologies. Necessary and sufficient conditions to characterize stabilizing consensus controllers are obtained. Then we consider the consensus for the multi-agent systems with switching interaction topologies based on control parametrization.
Partial Sums of Orthonormal Bases Preserving Positivity - and Martingales.
Past and Future
Path continuity and last exit distributions
Path decompositions for real Levy processes
Path properties of a class of locally asymptotically self similar processes.
Path transformations of first passage bridges.
Pathwise approximations of processes based on the fine structure of their filtrations
Path-wise solutions of stochastic differential equations driven by Lévy processes.
In this paper we show that a path-wise solution to the following integral equationYt = ∫0t f(Yt) dXt, Y0 = a ∈ Rd,exists under the assumption that Xt is a Lévy process of finite p-variation for some p ≥ 1 and that f is an α-Lipschitz function for some α > p. We examine two types of solution, determined by the solution's behaviour at jump times of the process X, one we call geometric, the other forward. The geometric solution is obtained by adding fictitious time and solving an associated...
Paul Lévy et l’arithmétique des lois de probabilités
Ce court texte reprend un exposé donné le 15 Décembre 2011 au Laboratoire de Probabilités et Modèles Aléatoires, lors d’une journée en hommage à Paul Lévy. On y rappellera comment des considérations sur l’arithmétique des lois de probabilités ont conduit Lévy à étudier les processus à accroissements indépendants.
PDE's for the Dyson, Airy and Sine processes
In 1962, Dyson showed that the spectrum of a random Hermitian matrix, whose entries (real and imaginary) diffuse according to independent Ornstein-Uhlenbeck processes, evolves as non-colliding Brownian particles held together by a drift term. When , the largest eigenvalue, with time and space properly rescaled, tends to the so-called Airy process, which is a non-markovian continuous stationary process. Similarly the eigenvalues in the bulk, with a different time and space rescaling, tend...
Penalisation of a stable Lévy process involving its one-sided supremum
Penalisation involving the one-sided supremum for a stable Lévy process with index α∈(0, 2] is studied. We introduce the analogue of Azéma–Yor martingales for a stable Lévy process and give the law of the overall supremum under the penalised measure.
Pénalisations de l’araignée brownienne
Dans cet article, nous pénalisons la loi d’une araignée brownienne prenant ses valeurs dans un ensemble fini de demi-droites concourantes, avec un poids égal à , où est un réel positif, une famille de réels indexés par , un paramètre réel, la distance de à l’origine, () la demi-droite sur laquelle se trouve , le temps local de à l’origine, et la constante de normalisation. Nous montrons que la famille des mesures de probabilité obtenue par ces pénalisations converge vers...