Asymptotic behaviors of randomly perturbed dynamical systems

Stochastic Analysis and Applications

Volumn 17, Issue 6, 1999, Pages 993-1008

  Lee, Oesook ^a  

^a Ewha Womans University   (South Korea)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033248042     PISSN: 07362994     EISSN: None     Source Type: Journal    
DOI: 10.1080/07362999908809646     Document Type: Article

References (19)

1. Barnsley, M.F. and Demko, S. Iterated function systems and the global construction of fractals. Proc.R. Soc. London A, 399(1985), 243-275.
2. Barnsley, M.F. and Elton. J.H. A new class of Markov processes for image encoding. Advanced Applied Probability, 20 (1988), 14-32.
3. Bhattacharya, R.N. and Lee, O. Ergodicity and central limit theorem for a class of Markov processes. Journal of Mutivariate Analysis. Vol.27, No. 1 (1988), 80-90.
4. Bhattacharya, R.N. and Waymire, E.C. Stochastic Processes and Applications. Wiley, New York, 1990.
5. Berger, M.A. Random affine iterated function systems: Mixing and encoding in Diffusion processes and related problems in analysis, vol.II, Stochastic flows. Birkhäuser, Boston, 1992.
6. Billingsley, P. Convergence of Probability Measures. Wiley, New York, 1968.
7. 2 convergence theorem for random affine mappings. J. Appl. Prob., 32 (1995), 183-192.
8. Dubin, L.E. and Freedman. D.A. Invariant probability for certain Markov processes. Ann. Math. Stat., 31 (1966), 837-848.
9. Elton, J.H. An ergodic theorem for terated maps. Ergod. Th.and Dynam.Sys. 7 (1987), 481-488.
10. Elton, J.H. and Piccioni, M. Iterated function systems arising from recursive estimation problems. Probability Theory and Related Fields. 91 (1992),103-114.
11. Feigin, P.D. and Tweedie, R.L. Random coefficient autoregressive processes: a Markov chain analysis of stationarity and finiteness of moments. J. Time Series Analy.,6 (1985), 1-14.
12. Furstenberg, H. and Kifer, Y. Random matrix products and measures on projective spaces. Israel J. Math., 46 (1983), 12-32.
13. Hewitt, E. and Stromberg, K. Real and Abstract Analysis. Springer-verlag, New York , 1965.
14. Kifer, Y. Ergodic Theory of Random Transformations. Birkhäuser, Boston, 1986.
15. Lasota, A. and Mackey, M. Stochastic perturbation of dynamical systems: The weak convergence of measures. Journal of Mathematical Analysis and Applications. 138 (1986), 232-248.
16. Lee, O. Limit theorems for some doubly stochastic processes. Statistics and Prob. Letters 32 (1997), 215-221.
17. Loskot., K. and Rudnicki, R. Limit theorems for stochastically perturbed dynamical systems. Journal of Applied Probability. 32 (1995), 459-469.
18. Nummelin, E. General Irreducible Markov Chains and Nonnegative Operators. Cambridge Univ. Press, Cambridge, 1984.
19. Tweedie, R.L. Criteria for rates of convergence of Markov chains with applications to queueing theory. Papers in Prob., Stat. and Analysis. J.F.C. Kingman and G.E.H. Reuter(eds.). Cambridge Univ.Press, Cambridge, pp. 260-276, 1983.