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

Tleubergenov, Marat Idrisovich; Ibraeva, Gulmira Temirgalikyzy

Eurasian Math. J. 10, No. 2, 93-102 (2019).

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.

MSC:

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

Keywords:

inverse problems; stochastic differential equations; integral manifolds

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