Mixing properties of Banach valued autoregressive processes (Q2748300)

The authors give sufficient conditions under which an autoregressive process, taking values in a Banach space \({\mathcal B}\), verifies absolute regularity and strong mixing. They consider first the process \(X_n=\rho X_{n-1}+\varepsilon_n\) where \(\rho\) is an operator taking values in \({\mathcal B}\) having norm bounded strictly by one and \(\varepsilon_n\) is a noise whose density verifies some regularity conditions. Then they extend their result to higher order autoregressive processes. The methods of proof strongly rely on those developed by \textit{A. Mokkaden} in 1990 to study the finite-dimensional case.