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 TMF, 1976, Volume 28, Number 3, Pages 371–380 (Mi tmf4273)

Construction of an exact solution of the Dyson equation for the mean value of the Green's function

O. V. Muzychuk

Abstract: A solution is found for the mean value of the Green's function of a stochastic linear system of general form with Gaussian fluctuating parameters. The method is based on constructing higher approximations of the Dyson equation by closing the chains of equations for the mean values of the variational derivatives of the solution at a certain step. It is shown that for the case of exponentially correlated fluctuations of the parameters of the system, the exact solution of the Dyson equation can be represented as an infinite continued fraction. The results are illustrated by the finding of the dynamical characteristics of an harmonic oscillator which has fluctuations of the eigenfrequency and the losses.

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English version:
Theoretical and Mathematical Physics, 1976, 28:3, 851–857

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Citation: O. V. Muzychuk, “Construction of an exact solution of the Dyson equation for the mean value of the Green's function”, TMF, 28:3 (1976), 371–380; Theoret. and Math. Phys., 28:3 (1976), 851–857

Citation in format AMSBIB
\Bibitem{Muz76} \by O.~V.~Muzychuk \paper Construction of an exact solution of the Dyson equation for the mean value of the Green's function \jour TMF \yr 1976 \vol 28 \issue 3 \pages 371--380 \mathnet{http://mi.mathnet.ru/tmf4273} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=449269} \transl \jour Theoret. and Math. Phys. \yr 1976 \vol 28 \issue 3 \pages 851--857 \crossref{https://doi.org/10.1007/BF01029178} 

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Citing articles on Google Scholar: Russian citations, English citations
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This publication is cited in the following articles:
1. S. E. Pitovranov, V. N. Chetverikov, “Corrections to the diffusion approximation in stochastic differential equations”, Theoret. and Math. Phys., 35:2 (1978), 415–422
2. G. I. Babkin, V. I. Klyatskin, “Analysis of the Dyson equation for stochastic integral equations”, Theoret. and Math. Phys., 41:3 (1979), 1080–1086
3. R. V. Bobrik, “Hierarchies of moment equations for the solution of the Schrödinger equation with random potential and their closure”, Theoret. and Math. Phys., 68:2 (1986), 841–847
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