Limit theorems for iterated random functions by regenerative methods

@inproceedings{Alsmeyer2001LimitTF,
  title={Limit theorems for iterated random functions by regenerative methods},
  author={Gerold Alsmeyer and Cheng-Der Fuh},
  year={2001}
}
Let (X, d) be a complete separable metric space and (F n) n≥0 a sequence of i.i.d. random functions from X to X which are uniform Lipschitz, that is, L n = sup x =y d(F n (x), F n (y))/d(x, y) < ∞ a.s. Providing the mean contraction assumption E log + L 1 < 0 and E log + d(F 1 (x 0), x 0) < ∞ for some x 0 ∈ X, it is known (see [4]) that the forward iterations M x n = F n • ... • F 1 (x), n ≥ 0, converge weakly to a unique stationary distribution π for each x ∈ X. The associated backward… CONTINUE READING
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