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References
R.S. Bucy: Stability and Positive Supermartingales, J. Diff. Eqs., vol.1, pp.151–155, (1965).
H.J. Kushner: Stochastic Stability and Control, Academic, N.Y. (1967).
F. Kozin: A Survey of Stability of Stochastic Systems, Automatica, vol.5, pp.95–112, Pergamon Press, (1969).
R.Z. Has'minskii: Stochastic Stability of Differential Equations, Sijthoff & Noordhoff, Maryland, (1980).
I.F. Blake and W.C. Lindsey: Level-Crossing Problems for Random Processes, IEEE Trans. Inf. Th., vol.IT-19, no.3, pp.295–315, (1973).
D.A. Darling and A.J.F. Siegert: The First Passage Problems for a Continuous Markov Process, Ann. Math Stat., vol.24, pp.624–639, (1953).
F. Kozin and S. Sugimoto: Determining Stability Properties of Stochastic Systems from Sample Observation, Proc. 1977 JACC, pp.1049–1055, (1977).
F. Kozin and S. Sugimoto: Decision Criteria for Stability of Stochastic Systems, Stochastic Problems in Dynamics, ed. by B.L. Clarkson, pp.8–35, Pitman, London, (1977).
Y. Sunahara: Stochastic Systems Theory, Inst. Electr. and Com. Eng. of Japan, Tokyo, in Japanese, (1979).
C.B. Mehr and J.A. Mcfadden: Certain Properties of Gaussian Processes and their First Passage Times, J. Roy. Statist. Soc. (B), pp.505–522, (1965).
I.I Gihman and A.V. Skorohod: Stochastic Differential Equations, Springer, N.Y., (1972).
R.Z. Khas'minskii: Necessary and Sufficient Conditions for the Asymptotic Stability of Linear Stochastic Systems, Th. Prob. Appls., vol.1. pp.144–147, (1967).
F. Kozin and S. Prodromou: Necessary and Sufficient Conditions for the Almost Sure Sample Stability of Linear Ito Equations, SIAM J. Appl. Math., vol.21, no.3, pp.413–424, (1971).
S. Sugimoto and F. Kozin: Some Properties on First Order Ito Systems and its Application to Finite Time Stochastic Stability Studies, Proc. 5th SICE Symp. on Contr. Th., pp.167–170, Hachioji, Tokyo, (1976).
S. Sugimoto: Relation between Sample and Moment Stability and Related Topics, Ph. D. Thesis, Dept. of Electr. Eng., Polytech. Inst. of New York, (1974).
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Sugimoto, S. (1982). A liapunov-like criterion and a first passage-time problems in non-linear stochastic systems. In: Drenick, R.F., Kozin, F. (eds) System Modeling and Optimization. Lecture Notes in Control and Information Sciences, vol 38. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0006164
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DOI: https://doi.org/10.1007/BFb0006164
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