Open AccessDifferential Equation in a Banach Space Multiplicatively Perturbed by Random Noise
Author(s) -
V. G. Zadorozhniy,
M. V. Konovalova
Publication year - 2017
Publication title -
sovremennaâ matematika. fundamentalʹnye napravleniâ
Language(s) - English
Resource type - Journals
eISSN - 2949-0618
pISSN - 2413-3639
DOI - 10.22363/2413-3639-2017-63-4-599-614
Subject(s) - mathematics , banach space , mathematical analysis , moment (physics) , space (punctuation) , order (exchange) , infinite dimensional vector function , pure mathematics , banach manifold , lp space , physics , linguistics , philosophy , finance , classical mechanics , economics
We consider the problem of nding the moment functions of the solution of the Cauchy problem for a rst-order linear nonhomogeneous dierential equation with random coecients in a Banach space. The problem is reduced to the initial problem for a nonrandom dierential 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.