Hostname: page-component-5c6d5d7d68-qks25 Total loading time: 0 Render date: 2024-08-26T13:58:43.634Z Has data issue: false hasContentIssue false
  • English
  • Français

A note on invariance principles for iterated random functions

Published online by Cambridge University Press:  14 July 2016

Ulrich Herkenrath ,
Marius Iosifescu  and
Andreas Rudolph
Ulrich Herkenrath
Affiliation:
Institut für Mathematik, Gerhard-Mercator-Universität Duisburg, D-47048 Duisburg, Germany. Email address: [email protected]
Marius Iosifescu
Affiliation:
Institute of Mathematical Statistics and Applied Mathematics, Casa Academiei Romane, Calea 13 Septembrie nr. 13, RO-76117 Bucharest 5, Romania
Andreas Rudolph
Affiliation:
Universität der Bundeswehr München, Werner-Heisenberg-Weg 39, D-85579 Neubiberg, Germany
Rights & Permissions [Opens in a new window]

Abstract

An abstract is not available for this content so a preview has been provided. As you have access to this content, a full PDF is available via the ‘Save PDF’ action button.
Image of the first page of this content. For PDF version, please use the ‘Save PDF’ preceeding this image.'
Type
Letter to the Editor
Information
Journal of Applied Probability , Volume 40 , Issue 3 , September 2003 , pp. 834 - 837
Copyright
Copyright © Applied Probability Trust 2003 

References

Benda, M. (1998). A central limit theorem for contractive stochastic dynamical systems. J. Appl. Prob. 35, 200–205.CrossRefGoogle Scholar
Billingsley, P. (1968). Convergence of Probability Measures. John Wiley, New York.Google Scholar
Borkovec, M. and Klüppelberg, C. (2001). The tail of the stationary distribution of an autoregressive process with ARCH(1)-errors. Ann. Appl. Prob. 11, 1220–1241.CrossRefGoogle Scholar
Diaconis, P., and Freedman, D. (1999). Iterated random functions. SIAM Rev. 41, 45–76.CrossRefGoogle Scholar
Durrett, R., and Resnick, S. I. (1978). Functional limit theorems for dependent variables. Ann. Prob. 6, 829–846.CrossRefGoogle Scholar
Elton, J. H. (1990). A multiplicative ergodic theorem for Lipschitz maps. Stoch. Process. Appl. 34, 39–47.CrossRefGoogle Scholar
Herkenrath, U., Iosifescu, M., and Rudolph, A. (2003). Random systems with complete connections and iterated function systems. Math. Rep. (Bucur.) 5, 127–140.Google Scholar
Heyde, C. C., and Scott, D. J. (1973). Invariance principles for the law of the iterated logarithm for martingales and processes with stationary increments. Ann. Prob. 1, 428–436.CrossRefGoogle Scholar
Lasota, A., and Yorke, J. A. (1994). Lower bound technique for Markov operators and iterated function systems. Random Comput. Dynamics 2, 41–77.Google Scholar
Scott, D. J. (1973). Central limit theorems for martingales and for processes with stationary increments, using a Skorokhod representation approach. Adv. Appl. Prob. 5, 119–137.CrossRefGoogle Scholar
Szarek, T. (1997). Markov operators acting on Polish spaces. Ann. Polon. Math. 67, 247–257.Google Scholar
Wu, W. B., and Woodroofe, M. (2000). A central limit theorem for iterated random functions. J. Appl. Prob. 37, 748–755.CrossRefGoogle Scholar