Locally contractive iterated function systems

Annals of Probability

Volumn 27, Issue 4, 1999, Pages 1952-1979

  Steinsaltz, David ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Iteration; Logistic maps; Lyapunov functions; Random attractors; Single server queues; Zeno's walk

Indexed keywords

EID: 0033233682     PISSN: 00911798     EISSN: None     Source Type: Journal    
DOI: 10.1214/aop/1022874823     Document Type: Article

References (19)

1. ABRAMOWITZ, M. and STEGUN, I. (1965). Handbook of Mathematical Functions, with Formulas, Graphs, and Mathematical Tables. Dover, New York.
2. ARNOLD, L., and CRAUEL, H. (1992). Iterated function systems and multiplicative ergodic theory. In Diffusion Processes and Related Problems in Analysis (M. Pinksy and V. Wihstutz, eds.) 2 283-305. Birkhäuser, Boston.
3. BACCELLI, F. and BREMAUD, P. (1994). Elements of Queueing Theory: Palm-Martingale Calculus and Stochastic Recurrences. Springer, New York.
4. BARNSLEY, M. F. and ELTON, J. H. (1988). A new class of Markov processes for image encoding. Adv. in App. Probab. 20 14-32.
5. CHAMAYOU, J. F. and LETAC G. (1991). Explicit stationary distributions for compositions of random functions and products of random matrices. J. Theoret. Probab. 4 3-36.
6. DEMBO, A. and ZEITOUNI, O. (1993). Large Deviation Techniques and Applications. Jones and Bartlett, Boston.
7. ELTON, J. H. (1990). A multiplicative ergodic theorem for Lipschitz maps. Stochastic Process. Appl. 34 39-47.
8. HUTCHINSON, J. E. Fractals and self-similarity. Indiana Univ. Math. J. 30 713-747.
9. KHASMINSKII, R. Z, (1990). Stochastic Stability of Differential Equations. Sijthoff & Noordhoff, Alphen aan den Rijn, Netherlands.
10. KIFER, Y. (1986). Ergodic Theory of Random Transformations. Birkhäuser, Boston.
11. LETAC, G. (1986). A contraction principle for certain Markov chains and its applications. Contemp. Math. 50 263-273.
12. LOYNES, R. (1962). The stability of queues with nonindependent interarrival and service times. Proc. Cambridge Philos. Soc. 58 497-520.
13. MEYN, S. and TWEEDIE, R. (1993). Markov Chains and Stochastic Stability. Springer, New York.
14. PROPP, J. and WILSON, D. (1998). Coupling from the past: a user's guide. In Microsurveys in Discrete Probability (D. Aidons and J. Propp, eds.) 181-192. Aer. Math. Soc., Providence, RI.
15. n (an Erdös problem). Ann. Math. 142 611-625.
16. STEINSALTZ, D. (1997). Zeno's walk: a random walk with refinements. Probab. Theory Related Fields 107 99-121.
17. STEINSALTZ, D. (1999). Random interval maps and Lyapunov exponents. Unpublished Manuscript.
18. STROOCK, D. W. (1993). Probability Theory, an Analytic View. Cambridge Univ. Press.
19. SHORACK, G. and WELLNEK, J. Empirical Processes with Applications to Statistics. Wiley, New York.