Das Gesetz vom iterierten Logarithmus mit Anwendungen auf die Zahlentheorie.
Degenerate limit laws for the maxima of trigonometric polynomials with random coefficients
Die Stoppverteilungen eines Markoff-Prozesses mit lokalendlichem Potential.
Differential operators and spectral distributions of invariant ensembles from the classical orthogonal polynomials. The continuous case.
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...
Equivalence theorems for infinite products of independent random elements on metric semigroups
Erratum : “Pathwise approximations of process based on the fine structure of their filtrations”
Espaces de cotype ,
Estimates of random walk exit probabilities and application to loop-erased random walk.
Exchangeable pairs and Poisson approximation.
Expected values in the alternative set theory and their applications to some limit theorems
This article presents an alternative approach to statistical moments within non-standard models and by the help of these moments some limit theorems are reformulated and proved.
Explicit bounds for the approximation error in Benford's law.
Exponential inequalities for sums of weakly dependent variables.
Fonctions harmoniques pour un opérateur de transition et applications
Further Results on Asymptotic Normality II.
Genealogies of regular exchangeable coalescents with applications to sampling
This article considers a model of genealogy corresponding to a regular exchangeable coalescent (also known as -coalescent) started from a large finite configuration, and undergoing neutral mutations. Asymptotic expressions for the number of active lineages were obtained by the author in a previous work. Analogous results for the number of active mutation-free lineages and the combined lineage lengths are derived using the same martingale-based technique. They are given in terms of convergence in...
Identically distributed pairs of partition statistics.
Iteration of random-valued functions on the unit interval
LAMN property for hidden processes : the case of integrated diffusions
In this paper we prove the Local Asymptotic Mixed Normality (LAMN) property for the statistical model given by the observation of local means of a diffusion process X. Our data are given by ∫01X(s+i)/n dμ(s) for i=0, …, n−1 and the unknown parameter appears in the diffusion coefficient of the process X only. Although the data are neither markovian nor gaussian we can write down, with help of Malliavin calculus, an explicit expression for the log-likelihood of the model, and then study the asymptotic...
Laws of large numbers for -statistics.