On r-quick convergence in the law of the interated logarithm for a class of dependent sequences.

Abstract

In this thesis we study Law of the Iterated Logarithm type properties for stationary *-mixing sequences of real random variables Xi infinityi=1 under certain moment conditions. Essentially we prove that under the assumption that all moments of X1 exist finitely then for any r > 0 we have an r-quick analogue to the functional form of the Law of the Iterated Logarithm. The treatment demonstrates the result directly from the asymptotic properties of the sequence. Several applications along the lines of those given by Strassen of the functional Law of the Iterated Logarithm are also presented.