AN INTRODUCTION TO FUNCTIONAL CENTRAL LIMIT-THEOREMS FOR DEPENDENT STOCHASTIC-PROCESSES

This paper shows how the modern machinery for generating abstract empi rical central limit theorems can be applied to arrays of dependent var iables. It develops a bracketing approximation (closely related to res ults of Philipp and Massart) based on a moment inequality for sums of strong mixing arrays, in an effort to illustrate the sorts of difficul ty that need to be overcome when adapting the empirical process theory for independent variables. Some suggestions for further development a re offered. The paper is largely self-contained.