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1 results

  • Limit theorems for iterated random functions

  • Part of
  • Wei Biao Wu, Xiaofeng Shao
  • Journal:
    Journal of Applied Probability / Volume 41 / Issue 2 / June 2004
    Published online by Cambridge University Press:
    14 July 2016, pp. 425-436
    Print publication:
    June 2004

  • 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.