Weak dependence for a class of local functionals of Markov chains on \(\mathbb Z^d\) (Q2822218)
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scientific article; zbMATH DE number 6630276
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Weak dependence for a class of local functionals of Markov chains on \(\mathbb Z^d\) |
scientific article; zbMATH DE number 6630276 |
Statements
27 September 2016
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Markov chain
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dynamical random environment
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central limit theorem
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math-ph
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math.MP
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Weak dependence for a class of local functionals of Markov chains on \(\mathbb Z^d\) (English)
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The authors consider a random walk in a dynamical random environment with mutual interaction introduced by \textit{C. Boldrighini} et al. [Ann. Inst. Henri Poincare, Probab. Stat. 30, No. 4, 519-558, 559--605 (1994; Zbl 0818.60063, Zbl 0818.60064)]. For this model, they prove a central limit theorem for sequences \(\{ f(S^k\hat{\eta})\}_{k=0}^\infty\), where \(S\) is the time shift, \(f\) is strictly local in space and belongs to a class of functionals related to the Hölder continuous functions on the torus, \(\hat{\eta}=\{ \eta_t\}_{t=0}^\infty\) is a Markov chain on \(\mathbb Z^d\).
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