WEAK INVARIANCE PRINCIPLE FOR MIXING SEQUENCES IN THE DOMAIN OF ATTRACTION OF NORMAL LAW

In this article we prove a weak invariance principle for a strictly stationary phi-mixing sequence {X-j}(j >= 1), whose truncated variance function L(x):=EX(1)(2)1({|X1|<= x}) is slowly varying at infinity and mixing coefficients satisfy the logarithmic growth condition: Sigma(n >= 1)phi(1/2)(2(n)) < infinity. This will be done under the condition that lim(n) Var (Sigma(n)(j=1) (X) over cap (j))/[Sigma(n)(j=1) Var((X) over cap (j))] = beta(2) exists in (0, infinity), where (X) over cap (j) = XjI{|Xj|<=eta j} and eta(2)(n) similar to nL(eta(n)).