Asymptotic equivalence of solutions of nonlinear It ô stochastic systems
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We investigate the problem of the asymptotic equivalence of systems of nonlinear ordinary and stochastic equations in mean square and with probability one.
KeywordsOrdinary Differential Equation Stochastic Differential Equation Strong Solution Stochastic System Functional Differential Equation
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- 1.L. Arnold, “Anticipative problems in the theory of random dynamical system in stochastic analysis,” in: M. Cranston and M. Pinsky (editors), Stochastic Analysis. AMS Proceeding of Symposia in Pure Mathematics, Vol. 57, American Mathematical Society, Providence, RI (1995), pp. 529–541.Google Scholar
- 3.V. K. Yasyns’kyi and E. V. Yasyns’kyi, Problems of Stability and Stabilization of Dynamical Systems with Finite Aftereffect [in Ukrainian], TViMS, Kyiv (2005).Google Scholar
- 5.R. Z. Khas’minskii, Stability of Systems of Differential Equations under Random Perturbations of Their Parameters [in Russian], Nauka, Moscow (1969).Google Scholar
- 6.V. K. Yasinskii, Stochastic Functional Differential Equations with Complete Prehistory [in Russian], TViMS, Kiev (2003).Google Scholar
- 7.H. L. Kulinich, Asymptotic Analysis of Unstable Solutions of One-Dimensional Stochastic Equations [in Ukrainian], Kyiv University, Kyiv (2003).Google Scholar
- 8.V.V. Buldygin, O. L. Klesov, and J.G. Steinebach, “PRV property and the asymptotic behavior of solutions of stochastic differential equations,” in: International Conference on Modern Problems and New Trends in Probability Theory (Chernivtsi, Ukraine, June 19–26, 2005), Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (2005), pp. 38–39.Google Scholar
- 9.V. I. Gikhman and A. V. Skorokhod, Stochastic Differential Equations [in Russian], Naukova Dumka, Kiev (1968).Google Scholar
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