Methods

Abstract

At present the methods for proving the limit theorems for dependent random variables can be subdivided into two types. The methods of the first type use the approximation with random variables, the asymptotic behaviour of which being known, for instance, the approximation with independent random variables (Bernstein’s method) or with ergodic martingale-differences (Gordin’s method). The methods of the second type use the direct approximation (Stein’s method, the classical methods of moments). In this book we are interested in a number of problems connected with c.l.th. and therefore we will demonstrate the methods using this example, though the applications of these methods are not exhausted by it.