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 Teor. Veroyatnost. i Primenen., 1961, Volume 6, Issue 1, Pages 130–138 (Mi tvp4760)

Short Communications

Evaluation of the One-Dimensional Probability Densities and Moments of a Random Process in the Output of an Essentially Non-Linear System

È. M. Khazen

Moscow

Abstract: This paper considers non-linear systems with feed-back. These systems contain non-linear functional transforms, which are separated by linear filters with rational spectra.
In order to evaluate the single-dimensional probability density and the moments of a random process in the output of the system, a multi-dimensional random Markov process is constructed, and the Kolmogorov diffusion equations are employed.
The exact results obtained by using this method are compared with the results of an approximate “statistical linearization” approach for one system. The two sets of results are found to agree well.

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English version:
Theory of Probability and its Applications, 1961, 6:1, 117–123

Citation: È. M. Khazen, “Evaluation of the One-Dimensional Probability Densities and Moments of a Random Process in the Output of an Essentially Non-Linear System”, Teor. Veroyatnost. i Primenen., 6:1 (1961), 130–138; Theory Probab. Appl., 6:1 (1961), 117–123

Citation in format AMSBIB
\Bibitem{Kha61} \by \E.~M.~Khazen \paper Evaluation of the One-Dimensional Probability Densities and Moments of a Random Process in the Output of an Essentially Non-Linear System \jour Teor. Veroyatnost. i Primenen. \yr 1961 \vol 6 \issue 1 \pages 130--138 \mathnet{http://mi.mathnet.ru/tvp4760} \transl \jour Theory Probab. Appl. \yr 1961 \vol 6 \issue 1 \pages 117--123 \crossref{https://doi.org/10.1137/1106016} `

• http://mi.mathnet.ru/eng/tvp4760
• http://mi.mathnet.ru/eng/tvp/v6/i1/p130

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