An addendum to ``A limitation of Markov representation for stationary processes'' (Q689185)

The paper is an addendum to an earlier paper by \textit{H. C. P. Berbee} and the author [ibid. 18, 33-45 (1984; Zbl 0545.60041)]. It is motived by the paper by \textit{W. Bryc} [ibid. 41, No. 2, 191-202 (1992; Zbl 0756.60027)] in which large deviations were proved for strictly stationary \(\varphi\)- mixing sequences whose mixing rate was faster than exponential. The purpose of the paper is to construct examples to indicate that such a mixing rate does not imply Markovian assumptions: Strictly stationary random sequences are constructed which satisfy \(\varphi\)-mixing condition with an arbitrarily fast mixing rate which cannot be represented as an instantaneous function of a strictly stationary real Harris recurrent Markov chain.