Geodesic
Moment functions for a solution of a stochastic system of partial differential equations
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh international spring mathematical school "Modern methods of the theory of boundary-value problems. Pontryagin readings—XXXIV", Voronezh, May 3-9, 2023, Part 2, Tome 231 (2024), pp. 53-67

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In this paper, we consider the Cauchy problem for a linear inhomogeneous system of first-order partial differential equations with two random coefficients and a random inhomogeneity. Explicit formulas for the moment functions of the solution are obtained: mathematical expectation, mixed moment functions, and the second moment function. As applications, explicit formulas for mixed moment functions and the second moment function for solutions of an equation with independent Gaussian random coefficients are obtained.
Keywords: system of first-order partial differential equations with random coefficients, mathematical expectation, mixed moment function, second moment function, variational derivative, characteristic functional 
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     title = {Moment functions for a solution of a stochastic system of partial differential equations},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {53--67},
     publisher = {mathdoc},
     volume = {231},
     year = {2024},
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L. Yu. Kabantosva. Moment functions for a solution of a stochastic system of partial differential equations. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh international spring mathematical school "Modern methods of the theory of boundary-value problems. Pontryagin readings—XXXIV", Voronezh, May 3-9, 2023, Part 2, Tome 231 (2024), pp. 53-67. http://geodesic.mathdoc.fr/item/INTO_2024_231_a4/