On inverse problem of closure of differential systems with degenerate diffusion. (English) Zbl 1463.34067

Summary: The quasi-inversion method is used to obtain necessary and sufficient conditions for the solvability of the inverse closure problem in the class of stochastic differential Itô systems of the first order with random perturbations from the class of processes with independent increments and diffusion degenerate with respect to a part of the variables.


34A55 Inverse problems involving ordinary differential equations
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
35F05 Linear first-order PDEs
34C45 Invariant manifolds for ordinary differential equations
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