CENTRAL-LIMIT-THEOREM, WEAK LAW OF LARGE NUMBERS FOR MARTINGALES IN BANACH-SPACES, AND WEAK INVARIANCE-PRINCIPLE - A QUANTITATIVE STUDY

JOURNAL OF MULTIVARIATE ANALYSIS

卷:52

Article

关键词: MODULUS OF CONTINUITY;    QUANTITATIVE RESULTS;    CENTRAL LIMIT THEOREM;    WEAK LAW OF LARGE NUMBERS;    MARTINGALES AND MARTINGALE DIFFERENCES IN BANACH SPACES;    WEAK INVARIANCE PRINCIPLE;    BROWNIAN MOTION;    WIENER PROCESS AND MEASURE;    GAUSSIAN DISTRIBUTION;    FRECHET DERIVATIVE;    BANACH SPACE;    C[0,1])-FUNCTIONS;    DEPENDENT RANDOM VARIABLES;    JACKSON-TYPE INEQUALITIES;    DECOMPOSABLE RANDOM VARIABLES;   

DOI  :  10.1006/jmva.1995.1009

来源: Elsevier

【 摘 要 】

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. (C) 1995 Academic Press. Inc.

【 授权许可】

Free