An invariance principle in L"2(0,1) for non stationary ?-mixing sequences

Abstract

Invariance principle in l"2(0,1) is studied using signed random measures. This approach to the problem uses an explicit isometry between L"2(0,1) and a reproducing kernel Hilbert space giving a very convenient setting for the study of compactness and convergence of the sequence of Donsker functions. As an application, we prove a L"2(0,1) version of the invariance in the case of ?-mixing random variables. Our result is not available in the D(0,1)-settingAvailable from Departamento de Matematica, Universidade de Coimbra, 3000 Coimbra, Portugal / FCT - Fundação para o Ciência e a TecnologiaSIGLEPTPortuga