Geodesic
Differential equation in a~Banach space multiplicatively perturbed by random noise
Contemporary Mathematics. Fundamental Directions, Differential and functional differential equations, Tome 63 (2017) no. 4, pp. 599-614.

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{CMFD_2017_63_4_a4,
     author = {V. G. Zadorozhniy and M. A. Konovalova},
     title = {Differential equation in {a~Banach} space multiplicatively perturbed by random noise},
     journal = {Contemporary Mathematics. Fundamental Directions},
     pages = {599--614},
     publisher = {mathdoc},
     volume = {63},
     number = {4},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CMFD_2017_63_4_a4/}
}
TY  - JOUR
AU  - V. G. Zadorozhniy
AU  - M. A. Konovalova
TI  - Differential equation in a~Banach space multiplicatively perturbed by random noise
JO  - Contemporary Mathematics. Fundamental Directions
PY  - 2017
SP  - 599
EP  - 614
VL  - 63
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CMFD_2017_63_4_a4/
LA  - ru
ID  - CMFD_2017_63_4_a4
ER  - 
%0 Journal Article
%A V. G. Zadorozhniy
%A M. A. Konovalova
%T Differential equation in a~Banach space multiplicatively perturbed by random noise
%J Contemporary Mathematics. Fundamental Directions
%D 2017
%P 599-614
%V 63
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CMFD_2017_63_4_a4/
%G ru
%F CMFD_2017_63_4_a4
V. G. Zadorozhniy; M. A. Konovalova. Differential equation in a~Banach space multiplicatively perturbed by random noise. Contemporary Mathematics. Fundamental Directions, Differential and functional differential equations, Tome 63 (2017) no. 4, pp. 599-614. http://geodesic.mathdoc.fr/item/CMFD_2017_63_4_a4/

[1] G. Adomian, Stochastic Systems, Mir, Moscow, 1987, Russian translation | MR

[2] A. A. Borovkov, Probability Theory, Nauka, Moscow, 1986 (in Russian) | MR

[3] I. M. Gel'fand, N. Ya. Vilenkin, Some Applications of Harmonic Analysis. Equipped Hilbert Spaces, FM, Moscow, 1961 (in Russian) | MR

[4] N. Dunford, J. T. Schwartz, Linear Operators, v. 1, General Theory, IL, M., 1962, Russian translation | MR

[5] V. G. Zadorozhniy, Methods of Variational Analysis, RKhD, Moscow–Izhevsk, 2006 (in Russian)

[6] V. I. Tikhonov, Stochastic Radio Engineering, Sov. Radio, Moscow, 1966 (in Russian)

[7] G. M. Fikhtengol'ts, A Course of Differential and Integral Calculus, v. 2, FM, Moscow, 1959 (in Russian)

[8] E. Hille, R. Phillips, Functional Analysis And Semi-Groups, IL, Moscow, 1962, Russian translation | MR