On the convergence in mean of martingale difference sequenceS
作者:
Paul Abraham,
John Alexopoulos,
S.J. Dilworth,
期刊:
Quaestiones Mathematicae
(Taylor Available online 2000)
卷期:
Volume 23,
issue 2
页码: 193-201
ISSN:1607-3606
年代: 2000
DOI:10.2989/16073600009485968
出版商: Taylor & Francis Group
数据来源: Taylor
摘要:
In [6] Freniche proved that any weakly null martingale difference sequence inL1[0, 1] has arithmetic means that converge in norm to 0. We show any weakly null martingale difference sequence in an Orlicz space whose N-function belongs to ∇3has arithmetic means that converge in norm to 0. Then based on a theorem in Stout [13, Theorem 3.3.9 (i) and (iii)], we give necessary and sufficient conditions for a bounded martingale difference sequence in an Orlicz space whose N-function belongs to a large class of ∇2functions to have means that converge to 0 a.s. Finally, we conclude with some expository comments including an easy proof of Komlos' theorem [9] forLp[0, 1], 1 < p < ∞.
点击下载:
PDF (164KB)
返 回