View in EDS

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

Saved in:
Bibliographic Details
Title: A precise upper bound for the error of interpolation of stochastic processes
Authors: Poganj, Tibor
Source: Theory of probability and mathematical statistics. 71:151-163
Publisher Information: 2005.
Publication Year: 2005
Subject Terms: almost sure reconstruction, mean-square reconstruction, sharp upper bound, truncation error, Sampling theorems, Kotel'nikov sums
Description: 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.
Document Type: Article
ISSN: 0094-9000
Accession Number: edsair.dris...01492..f5640dbc0d04d1c9ac83ded3452e2aab
Database: OpenAIRE
Description
Abstract: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