-norm of infinitely divisible random vectors and certain stochastic integrals.
La préservation des trajectoires du mouvement brownien et la préservation des lois de Cauchy
Le support des lois indefiniment divisibles dans un groupe Abelien localement compact.
Limit distributions for sums of shrunken random variables [Book]
Limit laws for products of free and independent random variables
We determine the distributional behavior of products of free (in the sense of Voiculescu) identically distributed random variables. Analogies and differences with the classical theory of independent random variables are then discussed.
Limit laws for transient random walks in random environment on
We consider transient random walks in random environment on with zero asymptotic speed. A classical result of Kesten, Kozlov and Spitzer says that the hitting time of the level converges in law, after a proper normalization, towards a positive stable law, but they do not obtain a description of its parameter. A different proof of this result is presented, that leads to a complete characterization of this stable law. The case of Dirichlet environment turns out to be remarkably explicit.
Limit theorems for Pareto-type distributions
Limit theorems for random fields [Book]
Limit theorems for randomly coarse grained continuous-time random walks [Book]
Limit theorems for some functionals with heavy tails of a discrete time Markov chain
Consider an irreducible, aperiodic and positive recurrent discrete time Markov chain (Xn,n ≥ 0) with invariant distribution μ. We shall investigate the long time behaviour of some functionals of the chain, in particular the additive functional S n = ∑ i = 1 n f ( X i ) for a possibly non square integrable functionf. To this end we shall link ergodic properties of the chain to mixing properties, extending known results in the continuous time case. We will then use existing results of convergence...
Limit theorems in free probability theory II
Based on an analytical approach to the definition of multiplicative free convolution on probability measures on the nonnegative line ℝ+ and on the unit circle we prove analogs of limit theorems for nonidentically distributed random variables in classical Probability Theory.
Lois indéfiniment divisibles et théorèmes de Ito-Nisio et Yuriskii
Lois stables dans un groupe
Lois stables et propriété de Slépian
Long memory and self-similar processes
This paper is a survey of both classical and new results and ideas on long memory, scaling and self-similarity, both in the light-tailed and heavy-tailed cases.