Abstract
For inhomogeneous systems of Itô stochastic differential equations, we introduce the notion of local invariance of surfaces and the notion of local first integral. We obtain results that give the general possibility of finding invariant surfaces and functionally independent first integrals of stochastic differential equations.
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REFERENCES
E. B. Dynkin, Markov Processes[in Russian], Fizmatgiz, Moscow (1963).
G. L. Kulinich and O. V. Pereguda, “Phase picture of the diffusion processes with the general diffusion matrices,” Random Oper. Stochast. Equat., 5, No.3, 203–216 (1997).
I. I. Gikhman and A. V. Skorokhod, Theory of Random Processes[in Russian], Vol. 3, Nauka, Moscow (1975).
I. I. Gikhman and A. V. Skorokhod, Stochastic Differential Equations[in Russian], Naukova Dumka, Kiev (1968).
V. G. Babchuk and G. L. Kulinich, “On one method for the determination of invariant sets of stochastic differential equations,” Teor. Ver. Primen., 23, No.2, 454 (1978).
R. Z. Khas'minskii, Stability of Systems of Differential Equations under Random Perturbations of Their Parameters[in Russian], Nauka, Moscow (1969).
A. M. Samoilenko, N. A. Perestyuk, and I. O. Parasyuk, Differential Equations[in Ukrainian], Lybid', Kiev (1994).
G. L. Kulinich, “Qualitative analysis of the influence of random perturbations on the phase velocity of harmonic oscillator,” Random Oper. Stochast. Equat., 3, No.2, 141–152 (1995).
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Kulinich, G.L., Pereguda, O.V. Qualitative Analysis of Systems of Itô Stochastic Differential Equations. Ukrainian Mathematical Journal 52, 1432–1438 (2000). https://doi.org/10.1023/A:1010332203269
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DOI: https://doi.org/10.1023/A:1010332203269