| 不同分布的卷积的局部封闭性及局部渐近性的充分条件和必要条件 |
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| 引用本文： | 刘希军,王岳宝. 不同分布的卷积的局部封闭性及局部渐近性的充分条件和必要条件[J]. 系统科学与数学, 2009, 29(4): 527-535 |
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| 作者姓名： | 刘希军 王岳宝 |
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| 作者单位： | 1. 刘希军,空军第一航空学院,信阳,464000
2. 王岳宝,苏州大学数学科学学院,苏州,215006 |
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| 摘 要： | 得到了支撑在[O,∞)上的不同分布的卷积(包括卷积根)的局部封闭性及局部渐近性的充分条件和必要条件,它揭示了不同分布的卷积及两两卷积之间的内在关系.这一结果的充分性部分推广了Geluk等非局部的相应结果,并且两者使用的方法是不同的;而这一结果的必要性部分是Geluk等人的结果中所没有的.最后,讨论了(-∞,∞)上不同分布卷积的局部封闭性及局部渐近性.
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| 关 键 词： | 卷积(卷积根) 局部次指数族 局部封闭性 局部渐近性 |
| 收稿时间： | 2007-04-13 |
The Sufficient Condition and Necessary Condition of Local Closure and Local Asymptotic for the Convolutions of Non-Identical Distributions |
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| LIU Xijun,WANG Yuebao. The Sufficient Condition and Necessary Condition of Local Closure and Local Asymptotic for the Convolutions of Non-Identical Distributions[J]. Journal of Systems Science and Mathematical Sciences, 2009, 29(4): 527-535 |
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| Authors: | LIU Xijun WANG Yuebao |
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| Affiliation: | (1)Department of Foundations, The First Aeronautical College of Air Force, Xinyang 464000; (2)Department of Mathematics, Soochow University, Suzhou 215006. |
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| Abstract: | This paper is concerned with some sufficient conditions and necessary conditions of local closure and local asymptotics for the convolutions (including convolution roots)of non-identical distributions on $[0,infty)$, which reveal the relations between convolutions and pairwise convolutions of non-identical distributions. The sufficient part of the result extends the corresponding non-local result of Geluk(2006), and the methods used here are different from theirs, the necessary part of the result is not included in the Geluk's paper. Finally, the local closure and local asymptotics for the convolutions of non-identical distributions on $(-infty,infty)$ are considered. |
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| Keywords: | Convolution(convolution root) local subexponential local closure local asymptotic. |
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