Central limit theorem, weak law of large numbers for martingales in banach spaces, and weak invariance principle - A quantitative study
Abstract
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.
Publication Title
Journal of Multivariate Analysis
Recommended Citation
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
