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Conditional convergence for randomly weighted sums of random variables based on conditional residual h-integrability
| Content Provider | Semantic Scholar |
|---|---|
| Author | Shen, Aiting Wu, Ranchao Chen, Yan Zhou, Yu |
| Copyright Year | 2013 |
| Abstract | Let {Xnk,un≤k≤vn,n≥1} and {Ank,un≤k≤vn,n≥1} be two arrays of random variables defined on the same probability space (Ω,A,P) and Bn be sub-σ-algebras of A. Let r>0 be a constant. In this paper, we introduce some concepts of conditional residual h-integrability such as conditionally residually h-integrable relative to Bn concerning the array {Ank} with exponent r and conditionally strongly residually h-integrable relative to Bn concerning the array {Ank} with exponent r. These concepts are more general than some known setting of randomly weighted sums of random variables. Based on the conditions of conditional residual h-integrability with exponent r and conditional strongly residual h-integrability with exponent r, we obtain the conditional mean convergence and conditional almost sure convergence for randomly weighted sums.MSC:60F15, 60F25. |
| Starting Page | 1 |
| Ending Page | 11 |
| Page Count | 11 |
| File Format | PDF HTM / HTML |
| DOI | 10.1186/1029-242X-2013-122 |
| Volume Number | 2013 |
| Alternate Webpage(s) | https://journalofinequalitiesandapplications.springeropen.com/track/pdf/10.1186/1029-242X-2013-122 |
| Alternate Webpage(s) | https://doi.org/10.1186/1029-242X-2013-122 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
