Stability of stochastic systems in the diffusion-approximation scheme

Ukrainian Mathematical Journal

Volumn 50, Issue 1, 1998, Pages 40-54

  Korolyuk, V S ^a  

^a INSTITUTE OF HYDROBIOLOGY   (Ukraine)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84879173495     PISSN: 00415995     EISSN: 15739376     Source Type: Journal    
DOI: 10.1007/BF02514687     Document Type: Article

References (19)

1. N. N. Bogolyubov, On Some Statistical Methods in Mathematical Physics [in Russian], Ukrainian Academy of Sciences, Kiev (1945).
2. Yu. A. Mitropol'skii and A M. Samoilenko. Mathematical Problems in Nonlinear Mechanics [in Russian], Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1987).
3. I. I. Gikhman, Differential Equations with Random Coefficients [in Russian], Ukrainian Academy of Sciences, Kiev (1964).
4. I. I. Gikhman. On Stability of Solutions of Stochastic Differential Equations [in Russian], Institute of Mathematics, Tashkent (1966).
5. A. V Skorokhod, Asymptotic Methods of the Theory of Stochastic Differential Equations, MMS Transl. Math. Monogr., Vol. 78 (1989).
6. A. M. Lyapunov, General Problem of Stability of Motion [in Russian], Gostekhizdat. Moscow (1950).
7. H. J. Kushner, Approximation and Weak Convergence Methods for Random Processes, MIT Press (1984).
8. J. Ya. Kac and N. N. Krasovskii, "About stability of systems with random parameters, " J. Appl. Math. Mech., 27, No. 5, 809-823 (1960)
9. R. Z. Khasminskii. "A limit theorem for the solutions with random right-hand side, " Theor. Probab. Appi, 11, 390-406 (1966). CrossRef
10. R. Z. Khasminskii, Stochastic Stability of Differential Equations, Simjthoff and Nordhoff (1980).
11. A. V. Skorokhod, "Dynamical systems under rapid random disturbances, " Ukr. Mat. Zh., 43, No. 1, 3-21 (1991). CrossRef
12. E. F. Tsarkov, "Average and stability of linear equations with small diffusion coefficients, " in: Proceedings of the VI USSR-Japan Symposium(1992), pp. 390-396.
13. E. F. Tsarkov. "On stability of solutions of linear differential equations with Markov coefficients, " Dokl. Akad. Nauk Ukr., No. 2, 34-37 (1987).
14. G. L. Blankenship and G C. Papanicolaou. "Stability and control of stochastic systems with wide band noise disturbances. I, " SIAM J. Appl. Math., 34, 437-476 (1978). CrossRef
15. V. S. Korolyuk, "Stability of autonomous dynamical systems with rapid Markov switchings, " Ukr. Mat. Zh., 43, No. 8, 1176-1181 (1991).
16. V. S. Korolyuk and A. V. Swishchuk, Evolution of Systems in Random Media, CRC Press (1995).
17. S. G. Krein, Linear Equations in Banach Spaces [in Russian], Nauka, Moscow (1971).
18. V. S. Korolyuk and A. F. Turbin, Mathematical Foundations of State Lumping Theory, Kluwer (1993).
19. V. S. Korolyuk and V. V. Korolyuk. Stochastic Models of Systems [in Russian], Naukova Dumka, Kiev (1989).