On some bidimensional denumerable chains of infinite order

We study homogeneous chains of infinite order ([xi]t)t[set membership, variant] with the set of states taken to be . Our approach is to interpret the half-infinite sequence ..., [xi]-n,..., [xi]-1, [xi]0, where as the continued fraction to the nearer integer expansion (read inversely) of a y [epsilon] [-,]. Thus, we are led to study certain Y-valued Markov chains, where Y = [-, ] and then by making use of their properties we establish the existence of denumerable chains of infinite order under conditions different from those given in Theorem 2.3.8 of Iosifescu-Theodorescu (1969). A (weak) variant of mixing is proved as well.