Some contributions to stochastic asymptotic stability and boundedness via multiple Lyapunov functions

Journal of Mathematical Analysis and Applications

Volumn 260, Issue 2, 2001, Pages 325-340

  Mao, Xuerong ^a  

^a UNIVERSITY OF STRATHCLYDE   (United Kingdom)

Author keywords

It 's formula; Limit set; Lyapunov functions; Supermartingale convergence theorem

Indexed keywords

EID: 0035882861     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jmaa.2001.7451     Document Type: Article

References (20)

1. Arnold L. Stochastic Differential Equations: Theory and Applications. 1972;Wiley, New York.
2. Arnold L., Crauel H., Wihstutz V. Stabilization of linear systems by noise. SIAM J. Control Optim. 21:1983;451-461.
3. Arnold L., Eizenberg A., Wihstutz V. Large noise asymptotics of invariant measures with application to Lyapunov exponents. Stochastics Stochastics Rep. 59:1996;71-142.
4. Elworthy K. D. Stochastic Differential Equations on Manifolds. 1982;Cambridge Univ. Press, Cambridge.
5. Friedman A., Pinsky M. Asymptotic stability and spiraling properties for solutions of stochastic equations. Trans. Amer. Math. Soc. 186:1973;331-358.
6. Hale J. K., Lunel S. M. V. Introduction to Functional Differential Equations. 1993;Springer-Verlag, New York/Berlin.
7. Has'minskii R. Z. Stochastic Stability of Differential Equations. 1981;Sijthoff & Noordhoff, Rockville.
8. Kolmanovskii V. B., Myshkis A. Applied Theory Functional Differential Equations. 1992;Kluwer Academic, Dordrecht.
9. Kushner H. J. Stochastic Stability and Control. 1967;Academic Press, San Diego.
10. Ladde G. S., Lakshmikantham V. Random Differential Inequalities. 1980;Academic Press, San Diego.
11. Lakshmikantham V., Leeda S., Martynyu A. Stability Analysis of Nonlinear Systems. 1989;Dekker, New York.
12. Lakshmikantham V., Matrosov V. M., Sivasundaram S. Vector Lyapunov Functions and Stability Analysis of Nonlinear Systems. 1991;Kluwer Academic, Dordrecht.
13. LaSalle J. P. Stability theory of ordinary differential equations. J. Differential Equations. 4:1968;57-65.
14. Lipster R. Sh., Shiryayev A. N. Theory of Martingales. 1989;Kluwer Academic, Dordrecht.
15. Mao X. Stability of Stochastic Differential Equations with Respect to Semimartingales. 1991;Longman, Harlow/New York.
16. Mao X. Exponential Stability of Stochastic Differential Equations. 1994;Dekker, New York.
17. Mao X. Stochastic Differential Equations and Applications. 1997;Ellis Horwood, Chichester.
18. Mao X. Stochastic versions of the LaSalle theorem. J. Differential Equations. 153:1999;175-195.
19. Mohammed S.-E. A. Stochastic Functional Differential Equations. 1986;Longman, Harlow/New York.
20. Salvadori L. Some contributions to asymptotic stability theory. Ann. Soc. Sci. Bruxelles. 88:1974;183-194.