Abstract
In this chapter, we will consider basic methods of determining statistical characteristics of solutions to stochastic equations.
Consider a linear (differential, integro-differential, or integral) stochastic equation. Averaging of such an equation over an ensemble of realizations of fluctuating parameters will not result generally in a closed equation for the corresponding average value. To obtain the closed equation, we must deal with an additional extended space whose dimension appears to be infinite in most cases. This approach makes it possible to derive the linear equation for average quantity of interest, but this equation will contain variational derivatives.
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© 2015 Springer International Publishing Switzerland
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Klyatskin, V.I. (2015). General Approaches to Analyzing Stochastic Dynamic Systems. In: Stochastic Equations: Theory and Applications in Acoustics, Hydrodynamics, Magnetohydrodynamics, and Radiophysics, Volume 1. Understanding Complex Systems. Springer, Cham. https://doi.org/10.1007/978-3-319-07587-7_8
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DOI: https://doi.org/10.1007/978-3-319-07587-7_8
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-07586-0
Online ISBN: 978-3-319-07587-7
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