Strong mixing of a stationary process (source code)

= Strong mixing of a stationary process
{title2=$\alpha(n)\longrightarrow0$}

Let $\mathcal F_{-\infty}^0$ and $\mathcal F_n^\infty$ be the sigma-algebras generated by the past and future observations. The mixing coefficient is $\alpha(n)=\sup_{A\in\mathcal F_{-\infty}^0,B\in\mathcal F_n^\infty}|P(A\cap B)-P(A)P(B)|$. Strong mixing means $\alpha(n)\to0$. Appropriate quantitative mixing and moment conditions can imply a <central limit theorem>; absolute summability of <autocovariance> alone does not.