We prove the existence of a weakly dependent strictly stationary solution of the equation Xt=F(Xt-1,Xt-2,Xt-3,...;[xi]t) called a chain with infinite memory. Here the innovations [xi]t constitute an independent and identically distributed sequence of random variables. The function F takes values...

Nous considérons une chaîne de Markov homogène {Xn}. Nous estimons la densité de sa probabilité de transition à l'aide d'estimateurs à noyaux. Nous appliquons ces méthodes à l'estimation de la fonction f, supposée inconnue, du processus défini par X1 et Xn+1 = f(Xn)+[var epsilon]n où...

We compare three dependence coefficients expressed in terms of conditional expectations, and we study their behaviour in various situations. Next, we give a new covariance inequality involving the weakest of those coefficients, and we compare this bound to that obtained by Rio (Ann. Inst. H....

Doukhan and Louhichi [P. Doukhan, S. Louhichi, A new weak dependence condition and application to moment inequalities, Stochastic Process. Appl. 84 (1999) 313-342] introduced a new concept of weak dependence which is more general than mixing. Such conditions are particularly well suited for...

The purpose of this paper is to propose a unifying weak dependence condition. Mixing sequences, functions of associated or Gaussian sequences, Bernoulli shifts as well as models with a Markovian representation are examples of the models considered. We establish Marcinkiewicz-Zygmund, Rosenthal...