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An estimate of the mean square error of interpolation of stochastic processes
Author(s):
A.
Ya.
Olenko
Translated by:
V. Semenov
Original publication:
Teoriya Imovirnostei ta Matematichna Statistika,
vipusk 72
(2005).
Journal:
Theor. Probability and Math. Statist.
No. 72
(2006),
113-123.
MSC (2000):
Primary 94A20, 60G12, 26D15;
Secondary 30D15, 41A05
Posted:
September 5, 2006
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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.
References:
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94A20, 60G12, 26D15,
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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:
10.1090/S0094-9000-06-00669-7
PII:
S 0094-9000(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):
3/JUL/2004
Posted:
September 5, 2006
Copyright of article:
Copyright
2006,
American Mathematical Society
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