Abstract:
The reflection coefficient is considered as a solution of a Cauchy boundary problem for a matrix Riccati differential equation. Variating of the Riccati equation leads to its linearization and permits to obtain the variation of the matrix reflection coefficient as a function of the variation of the real section length. A notion of dissipativity for the reflection coefficient is introduced. Under the dissipativity condition, statistical properties of the solution of the matrix Riccati differential equation are analyzed. The results obtained are compared with known theorems for non-dissipative transmission lines and with data of computer simulation for real transmission lines.
Citation:
M. H. Zakhar-Itkin, “On Statistics of the Reflection Coefficient of a Dissipative Multiwave Transmission Line with Random Section Lengths”, Teor. Veroyatnost. i Primenen., 18:2 (1973), 289–302; Theory Probab. Appl., 18:2 (1973), 281–294
\Bibitem{Zak73}
\by M.~H.~Zakhar-Itkin
\paper On Statistics of the Reflection Coefficient of a Dissipative Multiwave Transmission Line with Random Section Lengths
\jour Teor. Veroyatnost. i Primenen.
\yr 1973
\vol 18
\issue 2
\pages 289--302
\mathnet{http://mi.mathnet.ru/tvp4233}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=319465}
\zmath{https://zbmath.org/?q=an:0302.60068}
\transl
\jour Theory Probab. Appl.
\yr 1973
\vol 18
\issue 2
\pages 281--294
\crossref{https://doi.org/10.1137/1118030}
Linking options:
https://www.mathnet.ru/eng/tvp4233
https://www.mathnet.ru/eng/tvp/v18/i2/p289
This publication is cited in the following 5 articles:
“Summary of Papers Presented at Sessions of the Probability and Statistics Seminar in the Mathematical Institute of the USSR Academy of Sciences, 1977”, Theory Probab. Appl., 23:2 (1979), 439–457
S. V. Rezničenko, “The structure of the fundamental matrix of a system of coupled-mode equations”, Theory Probab. Appl., 22:2 (1978), 311–325
S. V. Rezničenko, “An investigation of systems of coupled-mode equations with small random disturbances”, Theory Probab. Appl., 22:1 (1977), 124–128
M. Kh. Zakhar-Itkin, “Ob ustoichivosti i ergodichnosti reshenii stokhasticheskogo
matrichnogo uravneniya Rikkati”, UMN, 31:3(189) (1976), 213–214
M. H. Zakhar-Itkin, “The matrix Riccati differential equation and the semi-group of linear fractional transformations”, Russian Math. Surveys, 28:3 (1973), 89–131
Citation in format AMSBIB
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