Nearby Variables with Nearby Conditional Laws and a Strong Approximation Theorem for Hilbert Space Valued Martingales
Abstract
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.
Document Details
- Document Type
- Technical Report
- Publication Date
- Apr 01, 1989
- Accession Number
- ADA225992
Entities
People
- D. Monrad
- W. Philipp
Organizations
- University of North Carolina at Chapel Hill