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
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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.
@article{TVP_2021_66_2_a3,
author = {V. G. Zadorozhniy},
title = {The expectation of a~solution of a~linear system of differential equations with random coefficients},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {284--304},
publisher = {mathdoc},
volume = {66},
number = {2},
year = {2021},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_2021_66_2_a3/}
}
TY - JOUR AU - V. G. Zadorozhniy TI - The expectation of a~solution of a~linear system of differential equations with random coefficients JO - Teoriâ veroâtnostej i ee primeneniâ PY - 2021 SP - 284 EP - 304 VL - 66 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TVP_2021_66_2_a3/ LA - ru ID - TVP_2021_66_2_a3 ER -
%0 Journal Article %A V. G. Zadorozhniy %T The expectation of a~solution of a~linear system of differential equations with random coefficients %J Teoriâ veroâtnostej i ee primeneniâ %D 2021 %P 284-304 %V 66 %N 2 %I mathdoc %U http://geodesic.mathdoc.fr/item/TVP_2021_66_2_a3/ %G ru %F TVP_2021_66_2_a3
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/