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Ultimate Boundedness of the Systems Governed by Stochastic Differential Equations

Published online by Cambridge University Press:  22 January 2016

Yoshio Miyahara
Yoshio Miyahara*
Affiliation:
Nagoya University
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The stability of the systems given by ordinary differential equations or functional-differential equations has been studied by many mathematicians. The most powerful tool in this field seems to be the Liapunov’s second method (see, for example [6]).

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 47 , September 1972 , pp. 111 - 144
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1972

References

[1] Gikhman, I. G. — Skorokhod, A. V., Introduction to the Theory of Random Processes, 1965.Google Scholar
[2] Nevel’son, M. B. and Khas’minskii, P. Z., Stability of Stochastic Systems, Problemy Peredachi Informatsii, vol. 2, No. 3, pp. 76–91, 1966.Google Scholar
[3] P. 3. 1969.Google Scholar
[4] Zakai, M., On the Ultimate Boundedness of Moments Associated with Solutions of Stochastic Differential Equations, SIAM J. Control, vol. 5, No. 4, 1967, pp. 588–593.Google Scholar
[5] Wonham, W. M., Liapunov Criteria for Weak Stochastic Stability, J. of Diff. Eq., 2, pp. 195–207, 1966.Google Scholar
[6] Krasovskii, N. N., Stability of Motion, Stanford Univ. Press, 1963.Google Scholar