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Theory of Probability and Mathematical Statistics

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Construction of the Karhunen-Loève model for an input Gaussian process in a linear system by using the output process


Authors: Yu. V. Kozachenko and I. V. Rozora
Translated by: N. N. Semenov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 99 (2018).
Journal: Theor. Probability and Math. Statist. 99 (2019), 113-124
MSC (2010): Primary 60G15, 68U20, 60K10
DOI: https://doi.org/10.1090/tpms/1084
Published electronically: February 27, 2020
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Abstract | References | Similar Articles | Additional Information

Abstract: We study a model of the input signal in a linear system for the case where the impulse response function is known. The output signal is the system response. We construct a model with the help of the Karhunen-Loève expansion that approximates the input process by using the output process with a given accuracy and reliability in the Banach space $ C ([0, T]) $. A partial case is considered where the input process is the Brownian motion.


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Additional Information

Yu. V. Kozachenko
Affiliation: Department of Probability Theory, Statistics, and Actuarial Mathematics, Faculty for Mechanics and Mathematics, Kyiv Taras Shevchenko National University, Volodymyrs’ka Street, 64/13, Kyiv 01601, Ukraine
Email: yvk@univ.kiev.ua

I. V. Rozora
Affiliation: Department of Applied Statistics, Faculty for Computer Science and Cybernetics, Kyiv Taras Shevchenko National University, Academician Glushkov, 4d, Kyiv 03680, Ukraine
Email: irozora@bigmir.net

DOI: https://doi.org/10.1090/tpms/1084
Keywords: Modeling, Gaussian process, Karhunen--Lo\`eve expansion, accuracy and reliability
Received by editor(s): July 30, 2018
Published electronically: February 27, 2020
Article copyright: © Copyright 2020 American Mathematical Society