This article is cited in 5 papers

Differential equation in a Banach space multiplicatively perturbed by random noise

V. G. Zadorozhniy, M. A. Konovalova

Voronezh State University, 1 Universitetskaya sq., 394006 Voronezh, Russia

Abstract: We consider the problem of finding the moment functions of the solution of the Cauchy problem for a first-order linear nonhomogeneous differential equation with random coefficients in a Banach space. The problem is reduced to the initial problem for a nonrandom differential equation with ordinary and variational derivatives. We obtain explicit formula for the mathematical expectation and the second-order mixed moment functions for the solution of the equation.

UDC: 517.97

DOI: 10.22363/2413-3639-2017-63-4-599-614