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# Monte Carlo Methods and Applications

Managing Editor: Sabelfeld, Karl K.

Editorial Board: Binder, Kurt / Bouleau, Nicolas / Chorin, Alexandre J. / Dimov, Ivan / Dubus, Alain / Egorov, Alexander D. / Ermakov, Sergei M. / Halton, John H. / Heinrich, Stefan / Kalos, Malvin H. / Lepingle, D. / Makarov, Roman / Mascagni, Michael / Mathe, Peter / Niederreiter, Harald / Platen, Eckhard / Sawford, Brian R. / Schmid, Wolfgang Ch. / Schoenmakers, John / Simonov, Nikolai A. / Sobol, Ilya M. / Spanier, Jerry / Talay, Denis

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1569-3961
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Volume 24, Issue 2

# On the modeling of linear system input stochastic processes with given accuracy and reliability

Iryna Rozora
• Corresponding author
• Department of Applied Statistics, Faculty of Computer Science and Cybernetics, Taras Shevchenko National University of Kyiv, 60 Volodymyrska Str., 01601 Kyiv, Ukraine
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• Other articles by this author:
• De Gruyter OnlineGoogle Scholar
/ Mariia Lyzhechko
• Department of Applied Statistics, Faculty of Computer Science and Cybernetics, Taras Shevchenko National University of Kyiv, 60 Volodymyrska Str., 01601 Kyiv, Ukraine
• Email
• Other articles by this author:
• De Gruyter OnlineGoogle Scholar
Published Online: 2018-04-15 | DOI: https://doi.org/10.1515/mcma-2018-0011

## Abstract

The paper is devoted to the model construction for input stochastic processes of a time-invariant linear system with a real-valued square-integrable impulse response function. The processes are considered as Gaussian stochastic processes with discrete spectrum. The response on the system is supposed to be an output process. We obtain the conditions under which the constructed model approximates a Gaussian stochastic process with given accuracy and reliability in the Banach space $C\left(\left[0,1\right]\right)$, taking into account the response of the system. For this purpose, the methods and properties of square-Gaussian processes are used.

MSC 2010: 60G15; 68U20; 60K10

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## About the article

Received: 2017-12-28

Accepted: 2018-03-31

Published Online: 2018-04-15

Published in Print: 2018-06-01

Citation Information: Monte Carlo Methods and Applications, Volume 24, Issue 2, Pages 129–137, ISSN (Online) 1569-3961, ISSN (Print) 0929-9629,

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© 2018 Walter de Gruyter GmbH, Berlin/Boston.

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