Abstract
We find an analytic representation of a solution of the Itô-Langevin equations in R 3 with orthogonal random actions with respect to the vector of the solution. We construct a stochastic process to which the integral of the solution weakly converges as a small positive parameter with the derivative in the equation tends to zero.
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References
V. A. Dubko, First Integral of a System of Stochastic Differential Equations [in Russian], Preprint No. 78-27, Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1978).
V. A. Dubko, Problems of the Theory of Stochastic Differential Equations and Their Applications [in Russian], Far Eastern Division of the Russian Academy of Sciences, Vladivostok (1989).
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 4, pp. 588–589, April, 1998.
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Dubko, V.A., Chalykh, E.V. Construction of an analytic solution for one class of Langevin-type equations with orthogonal random actions. Ukr Math J 50, 666–668 (1998). https://doi.org/10.1007/BF02487397
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DOI: https://doi.org/10.1007/BF02487397