Abstract
For a special class of systems of Itô stochastic equations with random coefficients, we establish conditions under which the modulus of the vector of state is not a random variable. We also consider possible ways of generalization of this problem.
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References
V. A. Dubko and E. V. Chalykh, “Construction of an analytic solution for one class of equations of the Langevin type with orthogonal random actions,” Ukr. Mat. Zh., 50, No. 4, 558–559 (1998).
V. A. Dubko, “Integral invariants, first integrals, and attracting manifolds of stochastic differential equations,” in: Nonlinear Problems of Mathematical Physics and Their Applications [in Russian], Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1998), pp. 103–106.
V. A. Dubko, “Open dynamical systems,” in: Searching for a Hidden Order [in Russian], Dal’nauka, Vladivostok (1995), pp. 94–115.
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 7, pp. 1004–1006, July, 1998.
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Chalykh, E.V. On one generalization of the Langevin equation with determinate modulus of velocity. Ukr Math J 50, 1145–1147 (1998). https://doi.org/10.1007/BF02528827
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DOI: https://doi.org/10.1007/BF02528827