A triangular central limit theorem under a new weak dependence condition

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 estimates under weak dependence. This extends on strong mixing and includes non-mixing Markov processes and associated or Gaussian sequences. We use Lindeberg method in Rio (Probab. Theory Related Fields 1996, 104, 255-282).