Robustness of iterated function systems of Lipschitz maps

Abstract Let $\{X_n\}_{n\in{\mathbb{N}}}$ be an ${\mathbb{X}}$ -valued iterated function system (IFS) of Lipschitz maps defined as $X_0 \in {\mathbb{X}}$ and for $n\geq 1$ , $X_n\;:\!=\;F(X_{n-1},\vartheta_n)$ where $\{\vartheta_n\}_{n \ge 1}$ are independent identically distributed random variables with common probability distribution $\mathfrak{p}$ $F(\cdot,\cdot)$ is continuous in the first variable, $X_0$ . Under parametric perturbation both F we interested robustness V -geometrical ergodicity property its invariant measure, finally $X_n$ Specifically, propose a pattern assumptions studying such properties IFS. This implemented autoregressive processes conditional heteroscedastic errors, IFS under roundoff error or thresholding/truncation. Moreover, provide general set covering classical Feller-type hypotheses to ergodic process. An accurate bound rate convergence also provided.