An L"2[0,1] invariance principle for LPQD random variables

Using an explicit isometry between Hilbert spaces and an embedding of the space of signed measures we prove an invariance principle with weak convergence in L"2[0,1] for random variables which are linearly positive quadrant dependent under type condition and some regularity on the covariance structureAvailable from Departamento de Matematica, Universidade de Coimbra, 3000 Coimbra, Portugal / FCT - Fundação para o Ciência e a TecnologiaSIGLEPTPortuga

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

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