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...
Eine Verallgemeinerung des Â?Gesetzes seltener Ereignisse".
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
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.
Ergodic properties of marked point processes in
Ergodic theorems for superadditive processes.
Ergodic theory of differentiable dynamical systems
Espacements multivariés généralisés et recouvrements aléatoires
Estimates in the laws of large numbers for regular summation methods.
Estimates of the rate of approximation in a de-poissonization lemma
Étude asymptotique d'une marche aléatoire centrifuge
Exact convergence rate for the maximum of standardized Gaussian increments.
Exact convergence rates in Erdös-Rényi type theorems for renewal processes
Exact laws for sums of ratios of order statistics from the Pareto distribution
Consider independent and identically distributed random variables {X nk, 1 ≤ k ≤ m, n ≤ 1} from the Pareto distribution. We select two order statistics from each row, X n(i) ≤ X n(j), for 1 ≤ i < j ≤ = m. Then we test to see whether or not Laws of Large Numbers with nonzero limits exist for weighted sums of the random variables R ij = X n(j)/X n(i).
Exact rate of convergence for increments of random fields.
Existence and asymptotic behaviour of some time-inhomogeneous diffusions
Let us consider a solution of a one-dimensional stochastic differential equation driven by a standard Brownian motion with time-inhomogeneous drift coefficient . This process can be viewed as a Brownian motion evolving in a potential, possibly singular, depending on time. We prove results on the existence and uniqueness of solution, study its asymptotic behaviour and made a precise description, in terms of parameters , and , of the recurrence, transience and convergence. More precisely, asymptotic...