On the solvability of the main inverse problem for a system of the first-order stochastic differential equations with degenerate diffusion
DOI:
https://doi.org/10.70474/579m1450Keywords:
stochastic differential equations, integral manifold, inverse problem, degenerate diffusionAbstract
The problem of constructing a system of first-order It\^{o} stochastic differential equations by the given properties of motion is considered. Necessary and sufficient conditions for the existence of a given integral manifold of the constructed equation are obtained in terms of the equation's coefficients. These conditions are derived separately for two cases: when the manifold depends on all independent variables and when it depends only on a part of variables.
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