Central limit theorems for iterated random Lipschitz mappings
By H. Hennion, Loïc Hervé. 2004
51 citations recorded by the source corpus.
Let M be a noncompact metric space in which every closed ball is compact, and let G be a semigroup of Lipschitz mappings of M. Denote by (Yn)n≥1 a sequence of independent G-valued, identically distributed random variables (r.v.’s), and by Z an M-valued r.v. which is independent of the r.v. Yn, n≥1. We consider the Markov chain (Zn)n≥0 with state space M which is defined recursively by Z0=Z and Zn+1=Yn+1Zn for n≥0. Let ξ be a real-valued function on G×M. The aim of this paper is to prove central limit theorems for the sequence of r.v.’s (ξ(Yn,Zn−1))n≥1. The main hypothesis is a condition of contraction in the mean for the action on M of the mappings Yn; we use a spectral method based on a quasi-compactness property of the transition probability of the chain mentioned above, and on a special perturbation theorem.
Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/aa152e412814650e931994761967f74f2a96d96e
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In Applied Mathematics
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Citations in the corpus
- Heavy tail phenomenon and convergence to stable laws for iterated Lipschitz maps (2009, methodology): “We start by introducing two Banach spaces Cρ(R) and Bρ,ǫ,λ(R) of continuous functions (23) (see also (16) and (17)).”