| 关于正则条件概率的几点注记 |
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| 引用本文： | 王志明,魏文晶. 关于正则条件概率的几点注记[J]. 武汉科技大学学报, 2015, 38(6): 475-477 |
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| 作者姓名： | 王志明 魏文晶 |
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| 作者单位： | 武汉科技大学理学院,湖北 武汉,430065,武汉科技大学理学院,湖北 武汉,430065 |
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| 基金项目： | 国家自然科学基金资助项目(61473213). |
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| 摘 要： | 本文证明了关于正则条件概率与正则条件期望的几个恒等式,并将所得结果应用到未必起始于固定点的Brown运动上,同时证明:一个Brown运动如果不起始于固定点而是起始于一个随机变量,则在关于初值的正则条件概率下,对于几乎所有的初值,该运动仍是Brown运动。
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| 关 键 词： | 正则条件 正则条件概率 条件概率 条件期望 条件分布 Brown运动 |
| 收稿时间： | 2015-09-13 |
Some notes on regular conditional probability |
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| Wang Zhiming and Wei Wenjing. Some notes on regular conditional probability[J]. Journal of Wuhan University of Science and Technology, 2015, 38(6): 475-477 |
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| Authors: | Wang Zhiming and Wei Wenjing |
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| Affiliation: | College of Science, Wuhan University of Science and Technology, Wuhan 430065, China and College of Science, Wuhan University of Science and Technology, Wuhan 430065, China |
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| Abstract: | This paper proves some identical equations concerning regular conditional probability and regular conditional expectation. The results are applied to Brownian motion not necessarily starting at a fixed point. It is demonstrated that, under the regular conditional probability about initial value, a Brownian motion with a random initial value instead of a fixed one is still a Brownian motion for almost all of the initial values. |
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| Keywords: | regularity condition regularity conditional probability conditional probability conditional expectation conditional distribution Brownian motion |
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