Large time decay behavior of dynamical equations with random perturbation features

Stochastic Analysis and Applications

Volumn 19, Issue 2, 2001, Pages 295-327

  Liu, Kai ^a   Mao, Xuerong ^b  

^a UNIVERSITY OF SHEFFIELD   (United Kingdom)

^b UNIVERSITY OF STRATHCLYDE   (United Kingdom)

Author keywords

Almost sure stability; Stochastic differential equations; Stochastic differential equations with time delays

Indexed keywords

EID: 0035531472     PISSN: 07362994     EISSN: None     Source Type: Journal    
DOI: 10.1081/SAP-100001190     Document Type: Article

References (20)

1. Arnold, L. Stochastic Differential Equations: Theory and Applications; Wiley: New York, 1974.
2. Bell, D.R.; Mohammed, E.A. On the Solution of Stochastic Ordinary Differential Equations via Small Delays. Stochastics. 1989, 29, 293-299.
3. Has'minskii, R.Z. Stochastic Stability of Differential Equations; Sijthoff and Noordhoff: Alphen, 1980.
4. Ladde, G.S.; Lakshmikantham, V. Random Differential Inequalities; Academic Press: New York, 1980.
5. Lakshmikantham, V.; Leeda, S.; Martynyuk, A.A. Stability Analysis of Nonlinear Systems; Marcel Dekker: New York, 1989.
6. Kolmanovskii, V.B.; Myshkis, A. Applied Theory of Functional Differential Equations; Kluwer Academic Publishers: Dordrecht, 1992.
7. Kolmonovskii, V.B.; Nosov, V.R. Stability of Functional Differential Equations; Academic Press: New York, 1986.
8. Chow, P.L. Stability of Nonlinear Stochastic Evolution Equations. J. Math. Anal. Appl. 1982, 89, 400-419.
9. Haussmann, U.G. Asymptotic Stability of the Linear Itô Equation in Infinite Dimensional. J. Math. Anal. Appl. 1978, 65, 219-235.
10. Ichikawa, A. Stability of Semilinear Stochastic Evolution Equations. J. Math. Anal. Appl. 1982, 90, 12-44.
11. Friedman, A. Stochastic Differential Equations and Applications; Academic Press: New York, 1975; Vols. 1/2.
12. Mao. X.R. Stability of Stochastic Differential Equations with Respect to Semimartingales, Pitman Research Notes in Mathematics Series 251; Longman Scientific and Technical: New York, 1991.
13. Friedman, A.; Pinsky, M. Asymptotic Stability and Spiraling Properties of Stochastic Equations. Trans. Amer. Math. Soc. 1973, 186, 331-358.
14. Liu, K On Stability for a Class of Semilinear Stochastic Evolution Equations. Stoch. Proc. Appl. 1997, 70, 219-241.
15. Arnold, L. A New Example of an Unstable System being Stabilized by Random Parameter Noise. Infor. Com. Math. Chem. 1979, 133-140.
16. Arnold, L.; Crauel, H.; Wihstutz, V. Stabilization of Linear Systems by Noise. SIAM J. Control Optim. 1983, 21, 451-461.
17. Has'minskii, R.Z. Necessary and Sufficient Conditions for the Asymptotic Stability of Linear Stochastic Systems. Theory Probab. Appl. 1969, 12, 144-147.
18. Lakshmikantham, V.; Matrosov, V.M.; Sivasundaram, S. Vector Lyapunov Functions and Stability Analysis of Nonlinear Systems; Kluwer Academic Publishers: Dordrecht, 1991.
19. Liu, K. Asymptotic Stability with General Rate Function of Nonlinear Stochastic Evolution Equations. J. Austral. Math. Soc. (Series A) 1997, 63, 128-144.
20. Mao, X.R. Exponential Stability of Stochastic Differential Equations; Marcel Dekker, Inc.: New York, 1994.