Nearby Variables With Nearby Conditional Laws and a Strong Approximation Theorem for Hilbert Space Valued Martingales.

摘要

This paper focuses on sequences of random vectors which do not admit a strong approximation of their partial sums by sums of independent random vectors. The first part proves conditional versions of the Strassen-Dudley theorem. These are applied to obtain strong invariance principles for vector-valued martingales which, when properly normalized, converge in law to a mixture of Gaussian distributions. Keywords: Mathematical models, Random variables. (cp)