Limit theorems for iterated random functions by regenerative methods
نویسندگان
چکیده
منابع مشابه
A Central Limit Theorem for Iterated Random Functions
A central limit theorem is established for additive functions of a Markov chain that can be constructed as an iterated random function. The result goes beyond earlier work by relaxing the continuity conditions imposed on the additive function, and by relaxing moment conditions related to the random function. It is illustrated by an application to a Markov chain related to fractals.
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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,...
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ژورنال
عنوان ژورنال: Stochastic Processes and their Applications
سال: 2001
ISSN: 0304-4149
DOI: 10.1016/s0304-4149(01)00104-1