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.