On strong mixing and Leadbetter's D condition

Abstract

Strong mixing is a condition which is often assumed to prove limit theorems for strictly stationary processes. Leadbetter's conditionD(un) is used to prove limit theorems for maxima of stationary processes.A sufficient condition for strong mixing to hold is given for the case where the process satisfies apth-order Markov property. This condition can be easy to check for whenpis small. This point is illustrated by two examples of first-order autoregressive processes.The conditionD(un) is shown to hold for any stationary Markov process.