An ergodic decomposition defined by transition probabilities (Q959993)
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scientific article; zbMATH DE number 5382716
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | An ergodic decomposition defined by transition probabilities |
scientific article; zbMATH DE number 5382716 |
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An ergodic decomposition defined by transition probabilities (English)
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16 December 2008
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The main goal of the present paper is to prove that any transition probability on a locally compact separable metric space \((X, d)\) defines a Kryloff--Bogoljubov--Beboutov--Yosida (KBBY) ergodic decomposition of the state space \((X,d)\). In the paper, elementary measures and standard elementary measures are defined. It is shown how these measures relate to the KBBY decomposition. The role played by the ergodic invariant probability measures in the decomposition is investigated. The KBBY decomposition for a fairly large class of transition functions is outlined.
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Markov operators
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ergodic decomposition
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ergodic invariant probability measures
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0.7569546699523926
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0.7507241368293762
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