Bickel, Peter J.Peter J.BickelLindner, MarkoMarkoLindner2021-10-252021-10-252012-05-28Theory of Probability and its Applications 56 (1): 1-20 (2012-05-28)http://hdl.handle.net/11420/10574In the first part of this paper we give an elementary proof of the fact that if an infinite matrix A, which is invertible as a bounded operator on ℓ 2, can be uniformly approximated by banded matrices, then so can the inverse of A. We give explicit formulas for the banded approximations of A -1 as well as bounds on their accuracy and speed of convergence in terms of their bandwidth. We then use these results to prove that the so-called Wiener algebra is inverse closed. In the second part of the paper we apply these results to covariance matrices ∑ of Gaussian processes and study mixing and beta mixing of processes in terms of properties of ∑. Finally, we note some applications of our results to statistics. © by SIAM.en1095-721920121120Gaussian stochastic processesHigh dimensional statistical inferenceInfinite band-dominated matricesMixing conditionsMathematikJournal Article10.1137/S0040585X97985224Other