Heavy tail phenomenon and convergence to stable laws for iterated Lipschitz maps

Mariusz Mirek

We consider the Markov chain $\{X_n^x{\}}_{n=0}^{\infty }$ on ${\mathbb{R}}^d$ defined by the stochastic recursion $X_{n}^{x}=\p_{θ_{n}}(X_{n-1}^{x})$, starting at $x\in {\mathbb{R}}^d$, where $θ_{1}, θ_{2}…