Iterates of expanding maps
Copyright policy )Iterates of expanding maps
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.
- Northampton Community College United States
- University of Zurich Switzerland
- University of Cambridge United Kingdom
- University of California, Los Angeles United States
- University of Oxford United Kingdom
Functional limit theorems; invariance principles, Gaussian approximations, 2603 Analysis, expanding map, Central limit and other weak theorems, iteration, 10123 Institute of Mathematics, Dynamical systems involving maps of the interval, 510 Mathematics, Stationary stochastic processes, Stein's method, 1804 Statistics, Probability and Uncertainty, 2613 Statistics and Probability, Expanding maps – Functional iteration – Coupling – Decay of correlations – Gaussian approximation
Functional limit theorems; invariance principles, Gaussian approximations, 2603 Analysis, expanding map, Central limit and other weak theorems, iteration, 10123 Institute of Mathematics, Dynamical systems involving maps of the interval, 510 Mathematics, Stationary stochastic processes, Stein's method, 1804 Statistics, Probability and Uncertainty, 2613 Statistics and Probability, Expanding maps – Functional iteration – Coupling – Decay of correlations – Gaussian approximation
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