Random perturbations of transformations of an interval (Q1821427)
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scientific article; zbMATH DE number 3998911
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Random perturbations of transformations of an interval |
scientific article; zbMATH DE number 3998911 |
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Random perturbations of transformations of an interval (English)
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1986
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The main result is as follows: Consider a map f of the interval [0,1] which is ergodic with invariant measure \(\mu_ f\), and a Markov chain \(x_ n^{\epsilon}\) with invariant measure \(\mu^{\epsilon}\) which is a small random perturbation of f. Then \(\mu^{\epsilon}\) converges weakly to \(\mu_ f\) as \(\epsilon\to 0\).
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stability
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invariant measure
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small random perturbation
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