Ergodic properties of weak asymptotic pseudotrajectories for semiflows

Journal of Dynamics and Differential Equations

Volumn 12, Issue 3, 2000, Pages 579-598

  Benaïm, Michel ^a   Schreiber, Sebastian J ^b  

^a UNIVERSITÉ DE CERGY PONTOISE   (France)

^b WESTERN WASHINGTON UNIVERSITY   (United States)

Author keywords

Asymptotic autonomous semiflows; Invariant measures; Minimal center of attraction; Stochastic algorithms; stochastic ordinary differential equation

Indexed keywords

EID: 0008202993     PISSN: 10407294     EISSN: 15729222     Source Type: Journal    
DOI: 10.1023/A:1026463628355     Document Type: Article

References (16)

1. Benaïm, M. (1996). A dynamical systems approach to stochastic approximations. SIAM J. Control Optim. 34, 437-472.
2. Benaïm, M., and Hirsch, M. W. (1995). Dynamics of Morse-Smale urn processes. Ergod. Theory Dynam. Syst. 15, 1005-1030.
3. Benaïm, M., and Hirsch, M. W. (1996). Asymptotic pseudotrajectories and chain recurrent flows, with applications. J. Dynam. Diff. Eq. 8, 141-176.
4. Duflo, M. (1996). Algorithmes Stochastiques, Mathématiques et Applications, Springer-Verlag, Berlin.
5. Durrett, R. (1991). Probability: Theory and Examples, Wadsworth and Brooks/Cole, Pacific Grove, California.
6. Friedman, A. (1975). Stochastic Differential Equations and Applications, Vol. 1, Academic Press, New York.
7. Hirsch, M. W., (1994). Asymptotic phase, shadowing and reaction-diffusion systems. In Differential Equations, Dynamical Systems and Control Science, Vol. 152, Lect. Notes Pure Appl. Math., Marcel Dekker, New York, pp. 87-99.
8. Katok, A., and Hasselblatt, B. (1997). Modern Theory of Dynamical Systems, Cambridge University Press, Cambridge.
9. Kushner, H. J., and Yin, G. G. (1997). Stochastic Approximation Algorithms and Applications, Springer-Verlag, New York.
10. Mischaikow, K., Smith, H., and Thieme, H. R. (1995). Asymptotically autonomous semiflows: Chain recurrence and Lyapunov functions. Trans. Am. Math. Soc. 347, 1669-1685.
11. Mañé, R. (1983). Ergodic Theory and Differentiable Dynamics, Springer-Verlag, New York.
12. Nemytskii, V. V., and Stepanov, V. V. (1960). Qualitative Theory of Differential Equations, Princeton University Press, Princeton, New Jersey.
13. Schreiber, S. J. (1997). Expansion rates and Lyapunov exponents. Discrete Conts. Dynam. Syst. 3, 433-438.
14. Stroock, D. W. (1993), Probability Theory. An Analytic View, Cambridge University Press, Cambridge.
15. Thieme, H. R. (1992). Convergence results and a Poincaré-Bendixson trichotomy for asymptotically autonomous differential equations. J. Math. Biol. 30, 755-763.
16. Thieme, H. R. (1994). Asymptotically autonomous differential equations in the plane. Rocky Mt. J. Math. 24, 351-380.