Weak Convergence of Laws on R with Common Marginals

In applications, it is often necessary to resort to approximations in the study of the properties of stochastic models. The original process can be replaced by a simpler one whose characteristics are already known or easier to study. This requires some stability of the model, which is usually represented in terms of integral probability metrics (Rachev, 1991, Müller, 1997). Among the many possible situations, a typical one is the difficulty to deal with the dependence properties of stochastic processes. For example, the study of the central limit problem for the standardised partial sum of dependent random variables requires the introduction of dependence conditions (mixing conditions, e.g. Doukhan, 1994, or weak dependence conditions, e.g. Doukhan and Louhichi, 1999). These dependence conditions are used to relate past and future realisations Aknowledgments: Partially supported by the ESRC Award RES 000-23-0400. Address for Correspondence: Faculty of Economics, Sidgwick Avenue, University of Cambridge, Cambridge CB3 9DE, UK. Tel.: +44(0)1223-335272; E-mail: [email protected].