Geodesic
On a system of differential equations with~random parameters
Contemporary Mathematics. Fundamental Directions, Differential and functional differential equations, Tome 68 (2022) no. 4, pp. 621-634

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An explicit formula for the mathematical expectation and second moment functions of a solution to a linear system of ordinary differential equations with a random parameter and a vector random right-hand side is obtained. The problem is reduced to the deterministic Cauchy problem for systems of first-order linear partial differential equations. We obtain an explicit formula for a solution of linear systems of partial differential equations of the first order with constant coefficients. An example is given showing that random factors can have a stabilizing effect on a linear system of differential equations.
Keywords: linear system of ordinary differential equations with a random parameter and a vector random right-hand side, moment functions, system of first-order linear partial differential equations, explicit solution. 
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     author = {V. G. Zadorozhniy and G. S. Tikhomirov},
     title = {On a system of differential equations with~random parameters},
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     pages = {621--634},
     publisher = {mathdoc},
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     number = {4},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CMFD_2022_68_4_a4/}
}
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V. G. Zadorozhniy; G. S. Tikhomirov. On a system of differential equations with~random parameters. Contemporary Mathematics. Fundamental Directions, Differential and functional differential equations, Tome 68 (2022) no. 4, pp. 621-634. http://geodesic.mathdoc.fr/item/CMFD_2022_68_4_a4/