| 次高斯情形下随机三角级数的几个重要结论 |
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| 引用本文： | 吴尚文.次高斯情形下随机三角级数的几个重要结论[J].北京建筑工程学院学报,2009,25(3):48-50. |
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| 作者姓名： | 吴尚文 |
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| 作者单位： | 北京建筑工程学院,理学院,北京,100044 |
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| 摘 要： | 利用重要不等式的研究方法，在∑n=0^∞xn^2〈∞这个条件下，对随机三角级数∑n=0^∞ξnxncos（nt＋Фn）（其中ξn是次正态随机变量序列）进行研究，得到了∑n=0^∞ξnxncos（nt＋Фn）几乎处处几乎必然收敛且此级数属于∩0〈p〈∞L^pa.s.的重要结论．
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| 关 键 词： | 次高斯变量 随机三角级数 几乎处处几乎必然收敛 Lp空间 |
Some Significant Conclusions of Random Trigonometric Series Under the Condition of Subgaussian Variables |
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| Wu Shangwen.Some Significant Conclusions of Random Trigonometric Series Under the Condition of Subgaussian Variables[J].Journal of Beijing Institute of Civil Engineering and Architecture,2009,25(3):48-50. |
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| Authors: | Wu Shangwen |
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| Affiliation: | Wu Shangwen (School of Science, BUCEA Beijing 100044) |
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| Abstract: | Using the methodology of important inequations, the random trigonometric series ∑n=0^∞ξnxncos（nt＋Фn） under the condition of ∑n=0^∞xn^2〈∞ are studied and some significant conclusions are obtained. ∑n=0^∞ξnxncos（nt＋Фn） is almost everywhere and almost surely convergent and ∑n=0^∞ξnxncos（nt＋Фn） belongs to ∩0〈p〈∞L^pa.s. |
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| Keywords: | subgaussian variables random trigonometric series almost everywhere and almost surely L^p space |
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