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Asymptotic behaviour of sample weighted circuits representing recurrent Markov chains

Published online by Cambridge University Press:  14 July 2016

S. Kalpazidou
S. Kalpazidou*
Affiliation:
Aristotle University of Thessaloniki
*
∗Postal address: Department of Mathematics, Faculty of Sciences, Aristotle University of Thessaloniki, 54006 Thessaloniki, Greece.
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Abstract

The asymptotic behaviour of the sequence (𝒞n(ω), wc,n(ω)/n), is studied where 𝒞n(ω) is the class of all cycles c occurring along the trajectory ωof a recurrent strictly stationary Markov chain (ξ n) until time n and wc,n(ω) is the number of occurrences of the cycle c until time n. The previous sequence of sample weighted classes converges almost surely to a class of directed weighted cycles (𝒞∞, ωc) which represents uniquely the chain (ξ n) as a circuit chain, and ω c is given a probabilistic interpretation.

Keywords

CIRCUIT CHAINSMULTIPLE MARKOV CHAINS
Type
Research Papers
Information
Journal of Applied Probability , Volume 27 , Issue 3 , September 1990 , pp. 545 - 556
Copyright
Copyright © Applied Probability Trust 1990 

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