Weak dependence : with examples and applications / Jérôme Dedecker, Paul Doukhan, Gabriel Lang ... [et al.]

The authors' goal is to provide a very general framework for the study of dependent variables. The main task is not only to provide the reader with the sharpest possible results but also to cover very general time series models. Two classes of sequences are considered. In case of "causal'' dependence, the conditions can be expressed in terms of conditional expectations. Sharp Donsker type results are derived using martingale theory. The second class contains "noncausal'' processes including two-sided linear processes. Moment inequalities are the main tools in this context. This book can be used as a textbook on weak dependence. It is based mostly on the most up-to-date results of the authors but the connection to the literature is also provided. The asymptotic results are used to derive several limit theorems for time series. (MathSciNet)