engleski

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

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.

Sampling theorems ; Kotel'nikov sums ; truncation error ; almost sure reconstruction ; mean-square reconstruction ; sharp upper bound

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