Iterates of expanding maps
Copyright policy )Iterates of expanding maps
Let \(h:I=[0,1]\to I\) be a piecewise monotone, \(C^1\) and uniformly expanding map. The authors are mainly interested in the iterates of \(h\). They show that the sequence of iterates can be closely tied to an \(m\)-dependent process. This provides good bounds on the accuracy of Gaussian approximations. To this end the authors use coupling and Stein's method.
- University of California, Los Angeles United States
- University of Zurich Switzerland
- University of Oxford United Kingdom
- University of Southern California United States
- Northampton Community College United States
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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