Limit Theorems for Iterated Random Functions

  title={Limit Theorems for Iterated Random Functions},
  author={WEI BIAOWU and Xiaofeng Shao},
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… CONTINUE READING
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