Mathematical expectation of the solution of a stochastic multiplicatively perturbed system of differential equations

L. Yu. Kabantosva

Voronezh State University, Voronezh, Russia

Abstract: 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.

UDC: 517.97

DOI: 10.22363/2413-3639-2023-69-2-250-262