On the solvability of the main inverse problem for stochastic differential systems. (English. Russian original) Zbl 1433.34031

Tleubergenov, M. I.; Ibraeva, G. T.

Ukr. Math. J. 71, No. 1, 157-165 (2019); translation from Ukr. Mat. Zh. 71, No. 1, 139-145 (2019).

Summary: By using the quasiinversion method, we establish necessary and sufficient conditions for the solvability of the main (according to Galiullin’s classification) inverse problem in the class of first-order Itô stochastic differential equations with random perturbations from the class of processes with independent increments with diffusion degenerated with respect to a part of variables and given properties depending on a part of variables.

MSC:

34A55	Inverse problems involving ordinary differential equations
34F05	Ordinary differential equations and systems with randomness
34C45	Invariant manifolds for ordinary differential equations

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