Geodesic
Mathematical expectation of the solution of a stochastic multiplicatively perturbed system of differential equations
Contemporary Mathematics. Fundamental Directions, Contemporary Mathematics. Fundamental Directions, Tome 69 (2023) no. 2, pp. 250-262

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We consider the Cauchy problem for a first-order linear inhomogeneous system of partial differential equations with random processes as coefficients. Explicit formulas for the mathematical expectation of the solution are obtained. Examples of systems with Gaussian and uniformly distributed random coefficients are considered. An example of calculations for a simplified learning model at the microlevel is given.
Keywords: first-order systems of partial differential equations with random coefficients, mathematical expectation, variational derivative, characteristic functional. 
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     author = {L. Yu. Kabantosva},
     title = {Mathematical expectation of the solution of a stochastic multiplicatively perturbed system of differential equations},
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     publisher = {mathdoc},
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     url = {http://geodesic.mathdoc.fr/item/CMFD_2023_69_2_a4/}
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L. Yu. Kabantosva. Mathematical expectation of the solution of a stochastic multiplicatively perturbed system of differential equations. Contemporary Mathematics. Fundamental Directions, Contemporary Mathematics. Fundamental Directions, Tome 69 (2023) no. 2, pp. 250-262. http://geodesic.mathdoc.fr/item/CMFD_2023_69_2_a4/