Statistical limit laws for equivariant observations.

Stochastics and Dynamics 4 (2004) 1-13.

Ian Melbourne and Matthew Nicol


Abstract

We show that statistical limit laws for ergodic stationary sequences of G-equivariant observations F(x,g) on a probability space X x G are inherited by sequences of observations F(x,g0) on the probability space X for each fixed g0. The statistical limit laws we consider are the central limit theorem, weak invariance principle and the law of the iterated logarithm.


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