Central limit theorem for a random dynamical system of affine transformations.Preprint Series # 913
AbstractWe 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 realvalued 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 $\mathbb{R}$.
