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Extensions of dynamical systems and the method of martingale approximation. (Russian. English summary) Zbl 0868.60011

Summary: Let \(T\) be a measure preserving transformation of a probability space \(({\mathcal X},{\mathcal F},\mu)\) and \(A\) be the generator of a \(\mu\)-symmetric Markov process with state space \(X\). Under the assumption that \(A\) is an “eigenvector” for \(T\), an extension of \(T\) is constructed in terms of \(A\). By means of this extension a version of the central limit theorem is proved via approximation by martingales.

MSC:

60B12 Limit theorems for vector-valued random variables (infinite-dimensional case)
60J35 Transition functions, generators and resolvents
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