Approximating the invariant measures of randomly perturbed dissipative maps

Journal of Mathematical Analysis and Applications

Volumn 198, Issue 2, 1996, Pages 534-551

  Hunt, Fern Y ^a  

^a NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030094524     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jmaa.1996.0097     Document Type: Article

References (20)

1. 1. F. Chatelin, "Spectral Approximation of Linear Operators," Academic Press, New York, 1983.
2. 2. C. Chiu, Q. Du, and T. Y. Li, Error estimates of the Markov finite approximation of the Frobenius-Perron operator, Nonlinear Analysis, 19, 2 (1992), 91-308.
3. 3. P. Collet, J. P. Eckmann, and O. E. Lanford III, Universal properties of maps on an interval, Comm. Math. Phys. 76 (1980), 211-254.
4. 4. J. L. Doob, "Stochastic Processes," Wiley, New York, 1953.
5. 5. N. Dunford and J. Schwartz, "Linear Operators," Part I, Wiley/Interscience, New York/London/Sydney, 1988.
6. 6. J. Guckenheimer, G. Oster, and A. Ipaktchi, The dynamics of density dependent population models, J. Math. Bio., 4 (1977), 101-147.
7. 7. F. Y. Hunt, A Monte Carlo approach to the approximation of invariant measures, Random and Comput. Dynamics 2 (1994), 111-133.
8. 8. F. Y. Hunt and W. M. Miller, On the approximation of invariant measures, J. Statist. Phys. 66, No. 1/2 (1992), 535-548.
9. 9. T. Kato, "Perturbation Theory for Linear Operators," Springer-Verlag, Berlin, 1976.
10. 10. Y. Kifer, "Random Perturbations of Dynamical Systems," Birkhaüser, Boston/Basel, 1988.
11. 11. U. Krengel, "Ergodic Theorems," de Gruyter, Berlin/New York, 1985.
12. 12. A. Lasota and M. Mackey, "Probabilistic Properties of Deterministic Systems," Cambridge Univ. Press, Cambridge/New York/Melbourne, 1985.
13. 13. A. Lasota and M. Mackey, Stochastic perturbation of dynamical systems: The weak convergence of measures, J. Math. Anal. Appl. 138 (1989), 232-248.
14. 14. R. S. MacKay, An extension of Zeeman's notion of structural stability to non-invertible maps, Physica D 52 (1991) 246-253.
15. 15. A. Lasota and J. Tyrcha, On the strong convergence to equilibrium for randomly perturbed dynamical systems, Ann. Pol. Mat. 53, No. 1 (1991), 79-89.
16. 16. T. Y. Li, Finite approximation for the Frobenius-Perron operator: A solution to Ulam's conjecture, J. Approx. Theory 17 (1976), 177-186.
17. 17. S. P. Meyn and R. L. Tweedie, "Markov Chains and Stochastic Stability," Springer-Verlag, London/Berlin/Heidelberg, New York, 1993.
18. 18. S. Ulam, "Problems in Modern Mathematics," Interscience Publishers, New York, 1960.
19. 19. K. Yosida and S. Kakutani, Operator-theoretical treatment of Markoff's process and mean ergodic theorem, Ann. Math. 42, No. 1 (1941), 188-228.
20. 20. E. C. Zeeman, Stability of dynamical systems, Nonlinearity 1 (1988), 115-155.