a1 Institut für Mathematische Stochastik, Universität Göttingen, Lotzestr. 13 D-3400 Gottingen, West Germany;
a2 Department of Mathematics, University of Illinois, Urbana, IL 61801, USA
Letdenote a flow built under a Hölder-continuous function l over the base (Σ, μ) where Σ is a topological Markov chain and μ some (ψ-mining) Gibbs measure. For a certain class of functions f with finite 2 + δ-moments it is shown that there exists a Brownian motion B(t) with respect to μ and σ2 > 0 such that μ-a.e.
for some 0 < λ < 5δ/588. One can also approximate in the same way by a Brownian motion B*(t) with respect to the probability. From this, the central limit theorem, the weak invariance principle, the law of the iterated logarithm and related probabilistic results follow immediately. In particular, the result of Ratner () is extended.
(Received August 05 1983)