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

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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/}
}
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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/