Doubly stochastic compound Poisson processes in extreme value theory.
Drift estimation from -mixing sequences.
Dynamical attraction to stable processes
We apply dynamical ideas within probability theory, proving an almost-sure invariance principle in log density for stable processes. The familiar scaling property (self-similarity) of the stable process has a stronger expression, that the scaling flow on Skorokhod path space is a Bernoulli flow. We prove that typical paths of a random walk with i.i.d. increments in the domain of attraction of a stable law can be paired with paths of a stable process so that, after applying a non-random regularly...
Dynamics of a continued fraction of Ramanujan with random coefficients.
Dynamics of Stochastic Neuronal Networks and the Connections to Random Graph Theory
We analyze a stochastic neuronal network model which corresponds to an all-to-all network of discretized integrate-and-fire neurons where the synapses are failure-prone. This network exhibits different phases of behavior corresponding to synchrony and asynchrony, and we show that this is due to the limiting mean-field system possessing multiple attractors. We also show that this mean-field limit exhibits a first-order phase transition as a function...
Dynamiques recuites de type Feynman-Kac : résultats précis et conjectures
Soit U une fonction définie sur un ensemble fini E muni d'un noyau markovien irréductible M. L'objectif du papier est de comparer théoriquement deux procédures stochastiques de minimisation globale de U : le recuit simulé et un algorithme génétique. Pour ceci on se placera dans la situation idéalisée d'une infinité de particules disponibles et nous ferons une hypothèse commode d'existence de suffisamment de symétries du cadre (E,M,U). On verra notamment que contrairement au recuit simulé, toute...
Edge occupation measure for a reversible Markov chain.
Edgeworth expansions for a sample sum from a finite set of independent random variables.
Effective WLLN, SLLN and CLT in statistical models
Weak laws of large numbers (WLLN), strong laws of large numbers (SLLN), and central limit theorems (CLT) in statistical models differ from those in probability theory in that they should hold uniformly in the family of distributions specified by the model. If a limit law states that for every ε > 0 there exists N such that for all n > N the inequalities |ξₙ| < ε are satisfied and N = N(ε) is explicitly given then we call the law effective. It is trivial to obtain an effective statistical...
Ein massentheoretisches Marginalproblem.
Eine Invarianzeigenschaft für Startverteilungen einer Klasse stochastischer Prozesse.
Eine Verallgemeinerung des Â?Gesetzes seltener Ereignisse".
Einführung des Wahrscheinlichkeitsoperators durch Postulate.
Einige Konvergenzprobleme bei Folgen von Martingalen.
Energy and the law of the interated logarithm.
Entropic Projections and Dominating Points
Entropic projections and dominating points are solutions to convex minimization problems related to conditional laws of large numbers. They appear in many areas of applied mathematics such as statistical physics, information theory, mathematical statistics, ill-posed inverse problems or large deviation theory. By means of convex conjugate duality and functional analysis, criteria are derived for the existence of entropic projections, generalized entropic projections and dominating points. Representations...
Entropie, théorèmes limite et marches aléatoires
Equivalence theorems for infinite products of independent random elements on metric semigroups
Ergodic and central limit theorems in statistical mechanics in continuous case
Ergodic averages with deterministic weights
We study the convergence of the ergodic averages where is a bounded sequence and a strictly increasing sequence of integers such that for some . Moreover we give explicit such sequences and and we investigate in particular the case where is a -multiplicative sequence.