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

Kozachenko, Yu.; Rozora, I.

doi:10.1090/tpms/1084

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
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
MathSciNet review: 3908660
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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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