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Marton, Katalin; Shields, Paul C.

The positive-divergence and blowing-up properties. (English) Zbl 0797.60044

Isr. J. Math. 86, No. 1-3, 331-348 (1994).
Summary: A property of ergodic finite-alphabet processes, called the blowing-up property, is shown to imply exponential rates of convergence for frequencies and entropy, which in turn imply a positive-divergence property. Furthermore, processes with the blowing-up property are finitely determined and the finitely determined property plus exponential rates of convergence for frequencies and for entropy implies blowing-up. It is also shown that finitary codings of i.i.d. processes have the blowing-up property.

Cited in 11 Documents

MSC:

60G99 Stochastic processes
60F99 Limit theorems in probability theory
94A17 Measures of information, entropy

Keywords:

ergodic finite-alphabet processes; exponential rates of convergence for frequencies; blowing-up property
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\textit{K. Marton} and \textit{P. C. Shields}, Isr. J. Math. 86, No. 1--3, 331--348 (1994; Zbl 0797.60044)
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