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

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Názov:	A precise upper bound for the error of interpolation of stochastic processes
Autori:	Poganj, Tibor
Zdroj:	Theory of probability and mathematical statistics. 71:151-163
Informácie o vydavateľovi:	2005.
Rok vydania:	2005
Predmety:	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
Prístupové číslo:	edsair.dris...01492..f5640dbc0d04d1c9ac83ded3452e2aab
Databáza:	OpenAIRE

Popis
Abstrakt:	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.
ISSN:	00949000