Limit Theorems under Generalized Mixing Conditions

Abstract

In /29/ Dobrushin has introduced some weak dependence conditions which represent a natural generalization of the mixing conditions for random fields. He suggested also that the c.l.th. which contains well-known results as a special case under these generalized mixing conditions holds. In this chapter a theorem of such type will be proved for s.r.p. with generalized α-mixing condition. Note that similar results may be obtained both for s.r.p. with generalized φ-mixing condition and for random fields. In the conclusion some generalizations of the c.l. th. will be given in case of so-called non-commutative probability theory.