Decay of correlations in one-dimensional dynamics
Density estimation for one-dimensional dynamical systems
In this paper we prove a Central Limit Theorem for standard kernel estimates of the invariant density of one-dimensional dynamical systems. The two main steps of the proof of this theorem are the following: the study of rate of convergence for the variance of the estimator and a variation on the Lindeberg–Rio method. We also give an extension in the case of weakly dependent sequences in a sense introduced by Doukhan and Louhichi.
Density Estimation for One-Dimensional Dynamical Systems
In this paper we prove a Central Limit Theorem for standard kernel estimates of the invariant density of one-dimensional dynamical systems. The two main steps of the proof of this theorem are the following: the study of rate of convergence for the variance of the estimator and a variation on the Lindeberg–Rio method. We also give an extension in the case of weakly dependent sequences in a sense introduced by Doukhan and Louhichi.
Dépassement des sommes partielles de v.a.r. indépendantes équidistribuées sans moment d'ordre 1
Dependent Lindeberg central limit theorem and some applications
In this paper, a very useful lemma (in two versions) is proved: it simplifies notably the essential step to establish a Lindeberg central limit theorem for dependent processes. Then, applying this lemma to weakly dependent processes introduced in Doukhan and Louhichi (1999), a new central limit theorem is obtained for sample mean or kernel density estimator. Moreover, by using the subsampling, extensions under weaker assumptions of these central limit theorems are provided. All the usual causal...
Depinning of a polymer in a multi-interface medium.
Determinantal processes and independence.
Determinism and martingale decompositions of strictly stationary random processes
Diffusion approximations of the geometric Markov renewal processes and option price formulas.
Discrete limit theorems for the Laplace transform of the Riemann zeta-function
In the paper discrete limit theorems in the sense of weak convergence of probability measures on the complex plane as well as in the space of analytic functions for the Laplace transform of the Riemann zeta-function are proved.
Distribuciones binomiales y de Bernoulli de probabilidad aleatoria. Teoremas del límite central.
Divergence Processes and Weak Convergence of Likelihood Ratio Processes
Doubly stochastic compound Poisson processes in extreme value theory.
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...