Asymptotics of stationary solutions of multivariate stochastic recursions with heavy tailed inputs and related limit theorems

Dariusz Buraczewski, Ewa Damek, Mariusz Mirek

Let ${\Phi }_n$ be an i.i.d. sequence of Lipschitz mappings of ${\mathbb{R}}^d$. We study the Markov chain $\{X_n^x{\}}_{n=0}^{\infty }$ on ${\mathbb{R}}^d$ defined by the recursion $X_n^x={\Phi }_n(X_{n-1}^x)$, $n\…