ON THE RATE OF CONVERGENCE IN THE INVARIANCE PRINCIPLE FOR DEPENDENT RANDOM VARIABLE SEQUENCE

In this paper, the speeds of convergence in Donsker’s invariance principle for partial processes contructed from the mixing partial sums S_n=\sum_i=1^n X_i is studied where prokhorov’s metrio is used to measure the distance between probability distribution on σ0, 1. For underlyiug nonstationary mixing variables which finite absolute moments of an order greater than two and less than four the rate obtained is analogous to that in the case of i.i.d.r.v.-s which is known to be that in （13）, but there Stationary and higher mixing speeds condition are required. The proof is used on the methods in （12）, and the martingale version of Skorohod’s embedding.