×
Yang, Wenzhi; Wang, Yiwei; Wang, Xinghui; Hu, Shuhe

Complete moment convergence for randomly weighted sums of martingale differences. (English) Zbl 1295.60056

J. Inequal. Appl. 2013, Paper No. 396, 13 p. (2013).
Summary: In this article, we obtain the complete moment convergence for randomly weighted sums of martingale differences. Our results generalize the corresponding ones for the nonweighted sums of martingale differences to the case of randomly weighted sums of martingale differences.

Cited in 9 Documents

MSC:

60G50 Sums of independent random variables; random walks
60F15 Strong limit theorems

Keywords:

complete convergence; randomly weighted sums; martingale differences
Cite Review PDF
Full Text: DOI

References:

[1] doi:10.1073/pnas.33.2.25 · Zbl 0030.20101 · doi:10.1073/pnas.33.2.25
[2] doi:10.1214/aoms/1177730037 · Zbl 0033.29001 · doi:10.1214/aoms/1177730037
[3] doi:10.1090/S0002-9947-1965-0198524-1 · doi:10.1090/S0002-9947-1965-0198524-1
[4] doi:10.1007/BF01045165 · Zbl 0698.60035 · doi:10.1007/BF01045165
[5] doi:10.1023/A:1022646429754 · Zbl 0913.60029 · doi:10.1023/A:1022646429754
[6] doi:10.1016/j.jmaa.2007.03.012 · Zbl 1130.60020 · doi:10.1016/j.jmaa.2007.03.012
[7] doi:10.1016/j.jmaa.2011.04.008 · Zbl 1237.60025 · doi:10.1016/j.jmaa.2011.04.008
[8] doi:10.1016/j.spl.2008.07.026 · Zbl 1154.60026 · doi:10.1016/j.spl.2008.07.026
[9] doi:10.1080/03610921003797761 · Zbl 1219.60034 · doi:10.1080/03610921003797761
[10] doi:10.1080/07362994.2011.548670 · Zbl 1217.60007 · doi:10.1080/07362994.2011.548670
[11] doi:10.1080/07362994.2012.649630 · Zbl 1237.60022 · doi:10.1080/07362994.2012.649630
[12] doi:10.1007/s11749-011-0248-0 · Zbl 1318.60036 · doi:10.1007/s11749-011-0248-0
[13] doi:10.1214/aos/1176347875 · Zbl 0721.62091 · doi:10.1214/aos/1176347875
[14] doi:10.1137/10078671X · Zbl 1219.93139 · doi:10.1137/10078671X
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.