ON THE INVARIANCE PRINCIPLE AND FUNCTIONAL LAW OF ITERATED LOGARITHM FOR NONERGODIC PROCESSES

Recently, nonergodic versions of several limit theorems for strictly stationary processes were given ([6], [7], [8]). The proofs were based on the fact that important properties of the stationary process which hold with respect to an invariant measure ＄￥mu＄ , are preserved with respect to its ergodic components. Using the same technique we shall prove two nonergodic versions of Heyde's functional CLT and log log law here