| 二叉分裂算法的随机路径长度 |
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| 引用本文： | 叶长青,苏淳,刘杰.二叉分裂算法的随机路径长度[J].中国科学技术大学学报,2007,37(3):225-228,254. |
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| 作者姓名： | 叶长青 苏淳 刘杰 |
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| 作者单位： | 中国科学技术大学统计与金融系,安徽合肥,230026 |
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| 基金项目： | 国家自然科学基金;中国科学院知识创新工程项目;中国科技大学校科研和教改项目 |
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| 摘 要： | 用泊松变换的方法研究了由二叉分裂算法所产生的随机树上的随机路径的长度,首次得到了关于其数学期望的确切表达式.在此基础上,对该期望的渐近性状进行了分析,证明了当被分裂的集合的大小n趋于无穷时,随机路径长度的期望具有log2n的阶.
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| 关 键 词： | 二叉分裂算法 双值和 泊松变换 指数逼近 随机路径 |
| 文章编号： | 0253-2778（2007）03-0225-04 |
| 修稿时间： | 2006-06-282006-12-01 |
The path length of the Bernoulli splitting algorithm |
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| YE Chang-qing,SU Chun,LIU Jie.The path length of the Bernoulli splitting algorithm[J].Journal of University of Science and Technology of China,2007,37(3):225-228,254. |
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| Authors: | YE Chang-qing SU Chun LIU Jie |
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| Institution: | Department of Statistics and Finance, University of Science and Technology of China, Hefei 230026, China |
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| Abstract: | The length of the random path generated by the Bernoulli splitting algorithm was studied by means of Poisson transformation.For the first time the exact expression of this expectation was obtained.Based on this expression,the asymptotic analysis of the expectation of the random path were presented.Thus it was proved that as the set size n goes to infinite,the expectation of the random path length has the order of log2n. |
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| Keywords: | Bernoulli splitting algorithm dyadic sum Poisson transform exponential approximation random path |
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