On the order of approximation in the random central limit theorem for m-dependent random variables

Abstrakt

We consider a random number Nn of m-dependent random variables Xk with a common distribution and the partial sums SNn = ∑Nn j=1 Xj , where the random variable Nn is independent of the sequence of random variables {Xk; k ≥ 1} for every n ≥ 1. Under certain conditions on the random variables Xk and Nn; we obtain the limit distribution of the sequence SNn and the corresponding rate of convergence after suitable normalization.