Mixing properties of a class of Bernoulli-processes

Abstract

We prove that stationary very weak Bernoulli processes with rate O ( 1 / n ) ( VWB O ( 1 / n ) ) O(1/n)\;({\text {VWB}}\,O(1/n)) are strictly very weak Bernoulli with rate O ( 1 / n ) O(1/n) . Furthermore we discuss the relation between VWB O ( 1 / n ) {\text {VWB}}\;O(1/n) and the classical mixing properties for countable state processes. In particular, we show that VWB O ( 1 / n ) {\text {VWB}}\,O(1/n) implies ϕ \phi -mixing.