Every ``lower psi-mixing'' Markov chain is ``interlaced rho-mixing'' (Q1965896)

The importance of mixing conditions for the central limit theory of weakly dependent random sequences is known, but the implications between various mixing conditions are not yet well established. The aim of the paper is to prove that for real-valued Markov chains, \(\psi '\)-mixing (a weaker version of \(\psi \)-mixing) implies \(\rho^*\)-mixing (an ``interlaced'' version of \(\rho \)-mixing). It is conjectured (but not proved) that every \(\varphi \)-mixing sequence (not even Markovian or stationary) is \(\rho ^*\)-mixing. A detailed discussion of mixing properties and implications is included.