Palm theory for random time changes.
Past and Future
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...
Perfect filtering and double disjointness
Perturbations ponctuelles d'évolutions : construction d'espaces stationnaires
Poincaré and log-Sobolev inequality for stationary Gaussian processes and moving average processes
For stationary Gaussian processes, we obtain the necessary and sufficient conditions for Poincaré inequality and log-Sobolev inequality of process-level and provide the sharp constants. The extension to moving average processes is also presented, as well as several concrete examples.
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,…)....
Positive operatorwertige Maβe und banachraumwertige stationäre Prozesse auf LCA-Gruppen
Prédiction scalaire ou prédiction vectorielle pour des processus faiblement stationnaires
Probabilistic properties of a Markov-switching periodic process
In this paper, we propose an extension of a periodic () model to a Markov-switching periodic (-), and provide some probabilistic properties of this class of models. In particular, we address the question of strictly periodically...
Problems from probability theory
Processus de Markov non stationnaires et espace-temps
Processus ponctuels stationnaires et flots spéciaux
Processus stationnaires et mesures de Palm du flot spécial sous une fonction
Proper moving average representations and outer functions in two variables.
Propriétés de mélange des processus autorégressifs polynomiaux
Propriétés markoviennes de processus sur R2