Self Diffusion of a tagged particle in equilibrium for asymmetric mean zero random walk with simple exclusion
Semi-martingales and rough paths theory.
Singleton independence
Motivated by the central limit problem for algebraic probability spaces arising from the Haagerup states on the free group with countably infinite generators, we introduce a new notion of statistical independence in terms of inequalities rather than of usual algebraic identities. In the case of the Haagerup states the role of the Gaussian law is played by the Ullman distribution. The limit process is realized explicitly on the finite temperature Boltzmannian Fock space. Furthermore, a functional...
Small positive values for supercritical branching processes in random environment
Branching Processes in Random Environment (BPREs) are the generalization of Galton–Watson processes where in each generation the reproduction law is picked randomly in an i.i.d. manner. In the supercritical case, the process survives with positive probability and then almost surely grows geometrically. This paper focuses on rare events when the process takes positive but small values for large times. We describe the asymptotic behavior of , as . More precisely, we characterize the exponential...
Some almost sure results for unbounded functions of intermittent maps and their associated Markov chains
We consider a large class of piecewise expanding maps T of [0, 1] with a neutral fixed point, and their associated Markov chains Yi whose transition kernel is the Perron–Frobenius operator of T with respect to the absolutely continuous invariant probability measure. We give a large class of unbounded functions f for which the partial sums of f○Ti satisfy both a central limit theorem and a bounded law of the iterated logarithm. For the same class, we prove that the partial sums of f(Yi) satisfy a...
Some applications of probability generating function based methods to statistical estimation
After recalling previous work on probability generating functions for real valued random variables we extend to these random variables uniform laws of large numbers and functional limit theorem for the empirical probability generating function. We present an application to the study of continuous laws, namely, estimation of parameters of Gaussian, gamma and uniform laws by means of a minimum contrast estimator that uses the empirical probability generating function of the sample. We test the procedure...
Some asymptotic properties of the hybrids of empirical and partial-sum processes.
Some exact rates in the functional law of the iterated logarithm
Some families of increasing planar maps.
Some Invariance Principles for Stochastic Processes and Their Inverse and Supremum Processes.
Stein’s method in high dimensions with applications
Let be a three times partially differentiable function on , let be a collection of real-valued random variables and let be a multivariate Gaussian vector. In this article, we develop Stein’s method to give error bounds on the difference in cases where the coordinates of are not necessarily independent, focusing on the high dimensional case . In order to express the dependency structure we use Stein couplings, which allows for a broad range of applications, such as classic occupancy,...
Stochastic Random Walk Summability.
Strong approximation for mixing sequences with infinite variance.
Strong limit theorems for a simple random walk on the 2-dimensional comb.
Sur la convergence des semimartingales vers un processus à accroissements indépendants
Sur la persistance du processus de Dawson-Watanabe stable. L'interversion de la limite en temps et de la renormalisation
Sur les déviations modérées des sommes de variables aléatoires vectorielles indépendantes de même loi
Testing the independence of two Poisson processes.
The almost sure invariance principle for the empirical process of U-statistic structure
The brownian cactus I. Scaling limits of discrete cactuses
The cactus of a pointed graph is a discrete tree associated with this graph. Similarly, with every pointed geodesic metric space , one can associate an -tree called the continuous cactus of . We prove under general assumptions that the cactus of random planar maps distributed according to Boltzmann weights and conditioned to have a fixed large number of vertices converges in distribution to a limiting space called the Brownian cactus, in the Gromov–Hausdorff sense. Moreover, the Brownian cactus...