LIMIT THEOREMS FOR CANONICAL VON MISES AND U-STATISTICS OF m-DEPENDENT OBSERVATIONS

The present paper continues the research started in the works of I. S. Borisov, A. A. Bystrov, and the author [Siberian Math. J., 47 (2006), pp. 980-989; Siberian Adv. Math., 18 (2008), pp. 244-259], where some limit theorems were proved for canonical U- and V -statistics based on stationary observations under psi-, phi-, or alpha-mixing. However, the conditions in the papers mentioned insure a certain limit behavior of these statistics and include either essential restrictions on finite dimensional distributions of the initial stationary sequence or some regularity conditions for kernels of the statistics under consideration. In the present work, it is shown that, in the case of stationary sequences of m-dependent observations, it is possible to remove the above-mentioned additional conditions while describing the limit behavior of U- and V -statistics.