Differential Equations in Banach Spaces Multiplicatively Perturbed by Random Noise

We consider the problem to find the moment functions of the solution of the Cauchy problem for a first-order linear inhomogeneous 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 va...

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Bibliographic Details
Published in:Journal of mathematical sciences (New York, N.Y.) N.Y.), 2021-12, Vol.259 (6), p.817-832
Main Authors: Zadorozhniy, V. G., Konovalova, M. A.
Format: Article
Language:English
Subjects:
Banach spaces
Cauchy problems
Differential equations
Mathematical analysis
Mathematics
Mathematics and Statistics
Random noise
Online Access:Get full text
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Summary:We consider the problem to find the moment functions of the solution of the Cauchy problem for a first-order linear inhomogeneous 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 expressions for the mathematical expectation and the second-order mixed moment functions for the solution of the equation.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-021-05664-0