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Theory of Probability and Mathematical Statistics

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An estimate of the mean square error of interpolation of stochastic processes


Author: A. Ya. Olenko
Translated by: V. Semenov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 72 (2005).
Journal: Theor. Probability and Math. Statist. 72 (2006), 113-123
MSC (2000): Primary 94A20, 60G12, 26D15; Secondary 30D15, 41A05
Published electronically: September 5, 2006
MathSciNet review: 2168141
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Abstract | References | Similar Articles | Additional Information

Abstract: For functions with an unbounded support of the spectrum, we obtain precise estimates of the error of interpolation by Whittaker-Kotelnikov-Shannon sums. We study the uniform and mean square errors of interpolation. Examples of extreme functions are given for which the estimate is precise. We obtain the rate of the mean square convergence of the error of interpolation for stochastic processes of the weak Cramér class and for processes generated by an orthogonal stochastic measure.


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Additional Information

A. Ya. Olenko
Affiliation: Department of Probability Theory and Mathematical Statistics, Faculty for Mathematics and Mechanics, National Taras Shevchenko University, Academician Glushkov Avenue, 6, Kyiv 03127, Ukraine
Email: olenk@univ.kiev.ua

DOI: https://doi.org/10.1090/S0094-9000-06-00669-7
Keywords: Errors of approximation/interpolation, extreme functions, Fr\'echet semivariation, convergence of random variables, unbounded spectrum, aliasing, Paley--Wiener function classes, Kotelnikov--Shannon theorem, precise estimate, upper estimate, interpolation, truncation error, stochastic processes, weak Cram\'er class
Received by editor(s): July 3, 2004
Published electronically: September 5, 2006
Article copyright: © Copyright 2006 American Mathematical Society