Abstract
New tools of statistical analysis for systems obeying differential equations in partial (and ordinary) derivatives with randomly alternating parameters of Markovian type and edge boundary conditions are presented. While the conventional master equation methods are valid only for the stochastic equations with given initial conditions, the method presented is more general and incorporates no embedding to an initial value problem. We develop a simple formalism by introduction of special double-sided conditional averages of dynamic variables. Its main advantage is that the averaging procedure for linear systems with multiplicative random influence is linear, yielding the possibility to obtain exact analytical solutions. The method is applied to a typical model of the theory of wave propagation in random media and exact results of its analysis are presented.
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