Precise lim sup behavior of probabilities of large deviations for sums of i.i.d. random variables.
Precise rates in log laws for NA sequences.
Precise small deviations in L 2 of some Gaussian processes appearing in the regression context
We find precise small deviation asymptotics with respect to the Hilbert norm for some special Gaussian processes connected to two regression schemes studied by MacNeill and his coauthors. In addition, we also obtain precise small deviation asymptotics for the detrended Brownian motion and detrended Slepian process.
Predictability, entropy and information of infinite transformations
We show that a certain type of quasifinite, conservative, ergodic, measure preserving transformation always has a maximal zero entropy factor, generated by predictable sets. We also construct a conservative, ergodic, measure preserving transformation which is not quasifinite; and consider distribution asymptotics of information showing that e.g. for Boole's transformation, information is asymptotically mod-normal with normalization ∝ √n. Lastly, we show that certain ergodic, probability preserving...
Prediction sequences in smooth Banach spaces
Principe de grandes déviations en théorie du filtrage non linéaire et algèbres de Lie Nilpotentes
Principe d'invariance sur le processus de vraisemblance
Principes d'invariance pour la probabilité d'un dilaté de l'enveloppe convexe d'un échantillon
Principes d'invariance pour les flots diagonaux sur SL(d,R)/SL(d,Z)
Probabilistic representations of operator semigroups - A unifying approach.
Probabilités de présence dans un processus de branchement spatial markovien
Probabilities on contractible locally compact groups : the existence of universal distributions in the sense of W. Doeblin
Problèmes de recouvrement et points exceptionnels pour la marche aléatoire et le mouvement brownien
La marche aléatoire (ou marche au hasard) est un objet fondamental de la théorie des probabilités. Un des problèmes les plus intéressants pour la marche aléatoire (ainsi que pour le mouvement brownien, son analogue dans un contexte continu) est de savoir comment elle recouvre des ensembles où se trouvent les points qui sont souvent (ou au contraire, rarement) visités, et combien il y a de tels points. Les travaux de Dembo, Peres, Rosen et Zeitouni permettent de résoudre plusieurs conjectures importantes...
Procédé de convergence minimale dans les espaces de Banach. Une loi des grands nombres et un théorème ergodique
Process level moderate deviations for stabilizing functionals
Functionals of spatial point process often satisfy a weak spatial dependence condition known as stabilization. In this paper we prove process level moderate deviation principles (MDP) for such functionals, which is a level-3 result for empirical point fields as well as a level-2 result for empirical point measures. The level-3 rate function coincides with the so-called specific information. We show that the general result can be applied to prove MDPs for various particular functionals, including...
Process-level large deviations for nonlinear Hawkes point processes
In this paper, we prove a process-level, also known as level-3 large deviation principle for a very general class of simple point processes, i.e. nonlinear Hawkes process, with a rate function given by the process-level entropy, which has an explicit formula.
Process-level quenched large deviations for random walk in random environment
We consider a bounded step size random walk in an ergodic random environment with some ellipticity, on an integer lattice of arbitrary dimension. We prove a level 3 large deviation principle, under almost every environment, with rate function related to a relative entropy.
Processus additifs positifs dans
Processus admettant un processus à accroissements indépendants tangent : cas général
Processus de Galton-Watson