Abstract
Let X be a Polish space and let S be a measurable space. Let {In} be a regenerative process with state space s. Take Z0 arbitrary but independent of {In}. We consider an iterated function system obtained recursively by Zn = FIn-1 (Zn-1)(n ≥ 1), where the function F : X × S → X defined by F(x, s) = Fs (x) is measurable and for each s ∈ S, Fs (x) is a continuous function of x. We obtain sufficient conditions under which, whatever the initial distribution, the functional central limit theorem holds.
Original language | English |
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Pages (from-to) | 1749-1759 |
Number of pages | 11 |
Journal | Indian Journal of Pure and Applied Mathematics |
Volume | 32 |
Issue number | 11 |
State | Published - Nov 2001 |
Keywords
- Functional central limit theorem
- Invariant probability
- Markov chain
- Regenerative process