Barbour, A D; Gerrard, R; Reinert, G (2000). Iterates of expanding maps. Probability Theory and Related Fields, 116(2):151-180.
The iterates of expanding maps of the unit interval into itself have many of the properties of a more conventional stochastic process, when the expanding map satisfies some regularity conditions and when the starting point is suitably chosen at random. In this paper, we show that the sequence of iterates can be closely tied to an m-dependent process. This enables us to prove good bounds on the accuracy of Gaussian approximations. Our main tools are coupling and Stein's method.
The iterates of expanding maps of the unit interval into itself have many of the properties of a more conventional stochastic process, when the expanding map satisfies some regularity conditions and when the starting point is suitably chosen at random. In this paper, we show that the sequence of iterates can be closely tied to an m-dependent process. This enables us to prove good bounds on the accuracy of Gaussian approximations. Our main tools are coupling and Stein's method.
| Item Type: | Journal Article, refereed, original work |
|---|---|
| Communities & Collections: | 07 Faculty of Science > Institute of Mathematics |
| Dewey Decimal Classification: | 510 Mathematics |
| Scopus Subject Areas: | Physical Sciences > Analysis
Physical Sciences > Statistics and Probability Social Sciences & Humanities > Statistics, Probability and Uncertainty |
| Uncontrolled Keywords: | Expanding maps – Functional iteration – Coupling – Decay of correlations – Gaussian approximation |
| Language: | English |
| Date: | 2000 |
| Deposited On: | 07 Apr 2010 13:02 |
| Last Modified: | 30 Jun 2022 17:41 |
| Publisher: | Springer |
| ISSN: | 0178-8051 |
| Additional Information: | The original publication is available at www.springerlink.com |
| OA Status: | Green |
| Publisher DOI: | https://doi.org/10.1007/PL00008725 |
Barbour, A D