La Trobe

Whittaker-Kotel'nikov-Shannon approximation of phi-sub-Gaussian random processes

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posted on 2025-05-29, 06:59 authored by Y Kozachenko, Andriy OlenkoAndriy Olenko
The article starts with generalizations of some classical results and new truncation error upper bounds in the sampling theorem for bandlimited stochastic processes. Then, it investigates Lp([0, T]) and uniform approximations of φ-sub-Gaussian random processes by finite time sampling sums. Explicit truncation error upper bounds are established. Some specifications of the general results for which the assumptions can be easily verified are given. Direct analytical methods are employed to obtain the results.

Funding

This research was partially supported under Australian Research Council's Discovery Projects funding scheme (project number DP160101366) and La Trobe University DRP Grant in Mathematical and Computing Sciences.

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History

Publication Date

2016-01-01

Journal

Journal of Mathematical Analysis and Applications

Volume

443

Issue

2

Pagination

21p. (p. 926-946)

Publisher

Elsevier

ISSN

1096-0813

Rights Statement

© 2016 The Authors. This manuscript version is made available under the CC-BY-NC-ND 4.0 license, whereby credit must be given to the creator, only noncommercial uses of the work are permitted and no derivatives or adaptations of the work are permitted: https://creativecommons.org/licenses/by-nc-nd/4.0/

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    Keywords

    Truncation error upper boundConvergence in Lp ([0, T])Uniform convergenceSub-Gaussian random processBandlimited stochastic processSampling theorem

    Licence

    CC BY-NC-ND 4.0

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