Mixing properties of a class of Bernoulli-processes

Abstract:

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