On Valiron and Circle Convergence.
On variance conditions for Markov chain CLTs.
On weak convergence of filtrations
On Weak Convergence of Parameter Estimators of General Statistical Parametric Models
On weak convergence of sequences of continuous local martingales
On weighted U-statistics for stationary random fields
The aim of this paper is to introduce a central limit theorem and an invariance principle for weighted U-statistics based on stationary random fields. Hsing and Wu (2004) in their paper introduced some asymptotic results for weighted U-statistics based on stationary processes. We show that it is possible also to extend their results for weighted -statistics based on stationary random fields.
Operator semigroups and Poisson convergence in selected metrics.
Orthogonal polynomial ensembles in probability theory.
Oscillation presque sûre de martingales continues
Parabolic Harnack inequality and local limit theorem for percolation clusters.
Parry expansions of polynomial sequences.
Penalization of the Wiener measure and principal values
Periodic transformations of the sample average reciprocal value
Perturbed random walks and Brownian motions, and local times.
Perturbed Toeplitz operators and radial determinantal processes
We study a class of rotation invariant determinantal ensembles in the complex plane; examples include the eigenvalues of Gaussian random matrices and the roots of certain families of random polynomials. The main result is a criterion for a central limit theorem to hold for angular statistics of the points. The proof exploits an exact formula relating the generating function of such statistics to the determinant of a perturbed Toeplitz matrix.
Physical measures for infinite-modal maps
We analyze certain parametrized families of one-dimensional maps with infinitely many critical points from the measure-theoretical point of view. We prove that such families have absolutely continuous invariant probability measures for a positive Lebesgue measure subset of parameters. Moreover, we show that both the density of such a measure and its entropy vary continuously with the parameter. In addition, we obtain exponential rate of mixing for these measures and also show that they satisfy the...
Planar Lorentz process in a random scenery
We consider the periodic planar Lorentz process with convex obstacles (and with finite horizon). In this model, a point particle moves freely with elastic reflection at the fixed convex obstacles. The random scenery is given by a sequence of independent, identically distributed, centered random variables with finite and non-null variance. To each obstacle, we associate one of these random variables. We suppose that each time the particle hits an obstacle, it wins the amount given by the random variable...
Poincaré Inequalities and Moment Maps
We discuss a method for obtaining Poincaré-type inequalities on arbitrary convex bodies in . Our technique involves a dual version of Bochner’s formula and a certain moment map, and it also applies to some non-convex sets. In particular, we generalize the central limit theorem for convex bodies to a class of non-convex domains, including the unit balls of -spaces in for .
Point processes of minimal order statistics
Pointwise ergodic theorems with rate and application to the CLT for Markov chains
Let T be Dunford–Schwartz operator on a probability space (Ω, μ). For f∈Lp(μ), p>1, we obtain growth conditions on ‖∑k=1nTkf‖p which imply that (1/n1/p)∑k=1nTkf→0 μ-a.e. In the particular case that p=2 and T is the isometry induced by a probability preserving transformation we get better results than in the general case; these are used to obtain a quenched central limit theorem for additive functionals of stationary ergodic Markov chains, which improves those of Derriennic–Lin and Wu–Woodroofe....