Central limit theorem and weak law of large numbers with rates for martingales in Banach spaces
This paper is concerned with large- error estimates concerning convergence in distribution as well as norm convergence for Banach space-valued martingale difference sequences. Indeed, two general limit theorems equipped with rates of convergence for such difference sequences are established. Applications of these lead to the central limit theorem and the weak law of large numbers with rates for Banach space-valued martingales.
Year of publication: |
1983
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Authors: | Butzer, P. L. ; Hahn, L. ; Roeckerath, M. Th. |
Published in: |
Journal of Multivariate Analysis. - Elsevier, ISSN 0047-259X. - Vol. 13.1983, 2, p. 287-301
|
Publisher: |
Elsevier |
Keywords: | General limit theorems convergence in distribution norm convergence large- rates of convergence martingale difference sequences in Banach spaces central limit theorem weak of large numbers [phi]-decomposability of random variables |
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