| 光滑平稳高斯过程极值几乎处处极限定理的一个推广 |
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| 引用本文： | 伍欣叶,吴群英.光滑平稳高斯过程极值几乎处处极限定理的一个推广[J].数学杂志,2015,35(6):1363-1371. |
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| 作者姓名： | 伍欣叶 吴群英 |
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| 作者单位： | 桂林理工大学理学院, 广西 桂林 541004,桂林理工大学理学院, 广西 桂林 541004 |
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| 基金项目： | Supported by National Natural Science Foundation of China (11061012; 11101101); the Natural Science Foundation of Guangxi (2012GXNSFAA053010; 2014GXNSFBA118023). |
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| 摘 要： | 本文研究了连续均方可微的平稳高斯过程的极限性态. 通过选择一个不同于Tan (2013) 的权重函数, 在较弱的条件下得到了连续均方可微平稳高斯过程极值的一个几乎必然仅限定理, 推广了Tan(2013) 的结论.
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| 关 键 词： | 平稳高斯过程 几乎处处 极限定理 极值 权重函数 |
| 收稿时间： | 2014/11/11 0:00:00 |
| 修稿时间： | 2015/1/20 0:00:00 |
AN EXTENSION OF THE ALMOST SURE LIMIT THEOREM FOR THE MAXIMA OF SMOOTH STATIONARY GAUSSIAN PROCESS |
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| WU Xin-ye and WU Qun-ying.AN EXTENSION OF THE ALMOST SURE LIMIT THEOREM FOR THE MAXIMA OF SMOOTH STATIONARY GAUSSIAN PROCESS[J].Journal of Mathematics,2015,35(6):1363-1371. |
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| Authors: | WU Xin-ye and WU Qun-ying |
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| Institution: | College of Science, Guilin University of Technology, Guilin 541004, China and College of Science, Guilin University of Technology, Guilin 541004, China |
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| Abstract: | In this paper, we study the limit behavior for the maxima of continuous mean square differentiable stationary Gaussian process. Using a different weight function from that in Tan (2013), we obtain an almost sure limit theorem for the maxima of continuous mean square differentiable stationary Gaussian process under some mild conditions, which expands the corre-sponding results in Tan (2013). |
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| Keywords: | stationary Gaussian process almost sure limit theorem maximum weight function |
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