Central limit theorem, weak law of large numbers for martingales in banach spaces, and weak invariance principle - A quantitative study
This article deals with quantitative results by involving the standard modulus of continuity in Banach spaces. These concern convergence in distribution for Banach space-valued martingale difference sequences and weak convergence of the distribution of random polygonal lines to the Wiener-measure on C([0, 1]). A general theorem is given with applications to the central limit theorem and weak law of large numbers for Banach space-valued martingales. Another general theorem is presented on the weak invariance principle with an application to a central limit theorem for real-valued martingales. The exposed results generalize earlier related results of Butzer, Hahn, Kirschfink, and Roeckerath. © 1995 Academic Press Inc.
Journal of Multivariate Analysis
Anastassiou, G. (1995). Central limit theorem, weak law of large numbers for martingales in banach spaces, and weak invariance principle - A quantitative study. Journal of Multivariate Analysis, 52 (1), 158-180. https://doi.org/10.1006/jmva.1995.1009