Geodesic
The expectation of a solution of a linear system of differential equations with random coefficients
Teoriâ veroâtnostej i ee primeneniâ, Tome 66 (2021) no. 2, pp. 284-304 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider a linear inhomogeneous system of differential equations of special form with three random coefficients defined by characteristic functionals. Operator functions generated by the functionals are introduced. The problem of finding the expectation of a solution of the Cauchy problem is reduced to the study of an auxiliary deterministic system of differential equations involving ordinary and variational derivatives. The solution of the resulting equation is written in terms of operator functions generated by the functionals. We derive explicit formulas for the expectation of the solution with uniformly distributed random coefficients, random Laplace coefficients, and Gaussian random coefficients.
Keywords: equations with random coefficients, variational derivative, stability in the mean, equations with variational derivatives, expectation. 
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V. G. Zadorozhniy. The expectation of a solution of a linear system of differential equations with random coefficients. Teoriâ veroâtnostej i ee primeneniâ, Tome 66 (2021) no. 2, pp. 284-304. http://geodesic.mathdoc.fr/item/TVP_2021_66_2_a3/

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