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On weak dependence conditions: The case of discrete valued processes

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<mark>Journal publication date</mark>11/2012
<mark>Journal</mark>Statistics and Probability Letters
Issue number11
Number of pages8
Pages (from-to)1941-1948
Publication StatusPublished
Early online date26/06/12
<mark>Original language</mark>English


We investigate the relationship between weak dependence and mixing for discrete valued processes. We show that weak dependence implies mixing conditions under natural assumptions. The results specialize to the case of Markov processes. Several examples of integer valued processes are discussed and their weak dependence properties are investigated by means of a contraction principle. In fact, we show the stronger result that the mixing coefficients for infinite memory weakly dependent models decay geometrically fast. Hence, all integer values models that we consider have weak dependence coefficients which decay geometrically fast.