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A precise upper bound for the error of interpolation of stochastic processes

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Název: A precise upper bound for the error of interpolation of stochastic processes
Autoři: Poganj, Tibor
Zdroj: Theory of probability and mathematical statistics. 71:151-163
Informace o vydavateli: 2005.
Rok vydání: 2005
Témata: almost sure reconstruction, mean-square reconstruction, sharp upper bound, truncation error, Sampling theorems, Kotel'nikov sums
Popis: We obtain a precise upper bound for the truncation error of interpolation of functions of the Paley-Wiener class with the help of finite Whittaker-Kotelnikov-Shannon sums. We construct an example of an extremal function for which the upper bound is achieved. We study the error of interpolation and the rate of the mean square convergence for stochastic processes of the weak Cramér class. The paper contains an extensive list of references concerning the upper bounds for errors of interpolation for both deterministic and stochastic cases. The final part of the paper contains a discussion of new directions in this field.
Druh dokumentu: Article
ISSN: 0094-9000
Přístupové číslo: edsair.dris...01492..f5640dbc0d04d1c9ac83ded3452e2aab
Databáze: OpenAIRE
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  Data: A precise upper bound for the error of interpolation of stochastic processes
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  Data: <i>Theory of probability and mathematical statistics</i>. 71:151-163
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  Data: 2005.
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  Data: 2005
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  Data: <searchLink fieldCode="DE" term="%22almost+sure+reconstruction%22">almost sure reconstruction</searchLink><br /><searchLink fieldCode="DE" term="%22mean-square+reconstruction%22">mean-square reconstruction</searchLink><br /><searchLink fieldCode="DE" term="%22sharp+upper+bound%22">sharp upper bound</searchLink><br /><searchLink fieldCode="DE" term="%22truncation+error%22">truncation error</searchLink><br /><searchLink fieldCode="DE" term="%22Sampling+theorems%22">Sampling theorems</searchLink><br /><searchLink fieldCode="DE" term="%22Kotel'nikov+sums%22">Kotel'nikov sums</searchLink>
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  Label: Description
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  Data: We obtain a precise upper bound for the truncation error of interpolation of functions of the Paley-Wiener class with the help of finite Whittaker-Kotelnikov-Shannon sums. We construct an example of an extremal function for which the upper bound is achieved. We study the error of interpolation and the rate of the mean square convergence for stochastic processes of the weak Cramér class. The paper contains an extensive list of references concerning the upper bounds for errors of interpolation for both deterministic and stochastic cases. The final part of the paper contains a discussion of new directions in this field.
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      – SubjectFull: almost sure reconstruction
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      – SubjectFull: mean-square reconstruction
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      – SubjectFull: sharp upper bound
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      – SubjectFull: truncation error
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      – SubjectFull: Sampling theorems
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      – SubjectFull: Kotel'nikov sums
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