Random Gaussian Markov sequences with values in a Hilbert space (Q1102021)
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scientific article; zbMATH DE number 4048742
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Random Gaussian Markov sequences with values in a Hilbert space |
scientific article; zbMATH DE number 4048742 |
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Random Gaussian Markov sequences with values in a Hilbert space (English)
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1986
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In the present paper we study infinite-dimensional Gaussian-Markov (g.m.) sequences. We describe the structure of stationary Gaussian Markov (g.m.) sequences; under certain restrictions on the conditional expectation operator we find necessary and sufficient conditions for the convergence in distribution and ergodicity of homogeneous Gaussian Markov (g.m.) sequences; these conditions are essentially different from Doeblin's condition and from the other known sufficient conditions for convergence and ergodicity of Markov chains.
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infinite-dimensional Gaussian-Markov (g.m.) sequences
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conditional expectation operator
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sufficient conditions for convergence
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ergodicity of Markov chains
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