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On the solvability of stochastic Helmholtz problem. (English. Russian original) Zbl 1467.34056

J. Math. Sci., New York 253, No. 2, 297-305 (2021); translation from Neliniĭni Kolyvannya 22, No. 3, 398-405 (2019).
In this paper, the authors consider inverse problems for differential systems in the presence of random perturbations. They employ the method of additional variables to establish sufficient conditions for the representation of stochastic differential equations of the second order in the form of stochastic Lagrange equations. Moreover, they establish the representation of stochastic differential equations of the first order in the form of stochastic canonical equations. Several examples are presented to illustrate the results obtained.

MSC:

34F05 Ordinary differential equations and systems with randomness
34A55 Inverse problems involving ordinary differential equations
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