Dynamic random evolutions on increasing time intervals (Q2849279)
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scientific article; zbMATH DE number 6208800
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Dynamic random evolutions on increasing time intervals |
scientific article; zbMATH DE number 6208800 |
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Dynamic random evolutions on increasing time intervals (English)
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17 September 2013
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dynamic random evolution
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averaging
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diffusion approximation
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large deviations
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exponential nonlinear operator
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The paper studies the asymptotic behavior of random evolutions in increasing time intervals by using solutions of the singular perturbation problem for reducible-invertible operators. The asymptotic behavior is studied in the scheme of series with a small parameter \(\varepsilon\), \(\varepsilon \to 0\). The paper establishes the averaging scheme or the law of large numbers, diffusion approximation or central limit theorem, and asymptotic behavior of large deviations or the exponential estimate of small probabilities. Each type of limit theorem corresponds to peculiar normalization condition given in terms of the small parameter.
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