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Limit theorems for iterated random functions

Limit theorems for iterated random functions We study geometric moment contracting properties of nonlinear time series that are expressed in terms of iterated random functions. Under a Dini-continuity condition, a central limit theorem for additive functionals of such systems is established. The empirical processes of sample paths are shown to converge to Gaussian processes in the Skorokhod space. An exponential inequality is established. We present a bound for joint cumulants, which ensures the applicability of several asymptotic results in spectral analysis of time series. Our results provide a vehicle for statistical inferences for fractals and many nonlinear time series models. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Applied Probability Cambridge University Press

Limit theorems for iterated random functions

Wu, Wei Biao; Shao, Xiaofeng
Journal of Applied Probability , Volume 41 (2): 12 – Jul 14, 2016
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Publisher
Cambridge University Press
Copyright
Copyright © Applied Probability Trust 2004 
ISSN
1475-6072
eISSN
0021-9002
DOI
10.1239/jap/1082999076
Publisher site
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Abstract

We study geometric moment contracting properties of nonlinear time series that are expressed in terms of iterated random functions. Under a Dini-continuity condition, a central limit theorem for additive functionals of such systems is established. The empirical processes of sample paths are shown to converge to Gaussian processes in the Skorokhod space. An exponential inequality is established. We present a bound for joint cumulants, which ensures the applicability of several asymptotic results in spectral analysis of time series. Our results provide a vehicle for statistical inferences for fractals and many nonlinear time series models.

Journal

Journal of Applied Probability – Cambridge University Press

Published: Jul 14, 2016

Keywords: Stationarity; iterated random function; central limit theorem; Dini continuity; exponential inequality; martingale; Markov chain; fractal; nonlinear time series; cumulants; 60F05; 60F17; 60J10; 60G42

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