# Central limit theorem for a random dynamical system of affine transformations.

Preprint Series # 913
Iwata, Yukiko Central limit theorem for a random dynamical system of affine transformations. (2008);

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## Abstract

We consider a random dynamical system of affine mappings of $\mathbb{R}$ with the generator $h(\omega,x):=a(\omega)x+b(\omega)$ where $x\in\mathbb{R}$ and $a$, $b$ are real-valued random variables on a probability space $(\Omega,\mathcal{F},P)$. Let $\theta:\Omega\to\Omega$ be an invertible ergodic transformation. In this paper we show central limit theorem for random processes $\{h(\theta^n\omega,x)\}_{n\geq 0}$ where $x$ is in some subset of $\mathbb{R}$.

Item Type: Preprint 20 random dynamical system; central limit theorem; stationary solution; ergodicity 60-xx PROBABILITY THEORY AND STOCHASTIC PROCESSES 1860