We use a new weak dependence condition from Doukhan and Louhichi (Stoch. Process. Appl. 1999, 84, 313-342) to provide a central limit theorem for triangular arrays; this result applies for linear arrays (as in Peligrad and Utev, Ann. Probab. 1997, 25(1), 443-456) and standard kernel density...

We investigate the relationship between weak dependence and mixing for discrete valued processes. We show that weak dependence implies mixing conditions under natural assumptions. The results specialize to the case of Markov processes. Several examples of integer valued processes are discussed...

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...