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On some bidimensional denumerable chains of infinite order

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  • Kalpazidou, Sofia

Abstract

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.

Suggested Citation

  • Kalpazidou, Sofia, 1985. "On some bidimensional denumerable chains of infinite order," Stochastic Processes and their Applications, Elsevier, vol. 19(2), pages 341-357, April.
    • Handle: RePEc:eee:spapps:v:19:y:1985:i:2:p:341-357
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