Appendix A
Ergodicity, Martingales, Mixing
A.1 Ergodicity
A stationary sequence Is said to be ergodic If it satisfies the strong law of large numbers.
Definition A.1 (Ergodic stationary processes) A strictly stationary process (Zt)t
realvalued, is said to be ergodic if and only if, for any Borel set B and any integer k,
with probability I.1
General transformations of ergodic sequences remain ergodic. The proof of the following result can be found, for instance, in Billingsley (1995, Theorem 36.4).
Theorem A.l If (Zt)t is an ergodic strictly stationary sequence and if(Yt)t is defined by
where f is a measurable function from ∞ to , then (Yt)t is also an ergodic strictly stationary sequence ...
