| 集值随机过程的均方Riemann-Stieljes积分 |
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| 引用本文： | 刘常昱,李世楷,周华任. 集值随机过程的均方Riemann-Stieljes积分[J]. 解放军理工大学学报(自然科学版), 2002, 3(3): 99-102 |
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| 作者姓名： | 刘常昱 李世楷 周华任 |
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| 作者单位： | 解放军理工大学,理学院,江苏,南京,211101;解放军理工大学,理学院,江苏,南京,211101;解放军理工大学,理学院,江苏,南京,211101 |
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| 摘 要： | 集值随机过程的积分理论是随机过程理论的一个新分支。利用随机集的位似及集值随机过程的均方收敛理论,创造性的定义了集值随机过程的均方Riemann-Stieljes积分,随后证明了均方Riemann-Stiel-jes积分存在性的判定定理,最后给出了分部积分计算公式,为今后进一步研究集值随机过程的微积分奠定了良好的理论基础。
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| 关 键 词： | 集值随机过程 均方收敛 均方Riemann-Stieljes积分 |
| 文章编号： | 1009-3443(2002)03-0099-04 |
Riemann -Stieljes Integral of the Set -valued Stochastic Processes |
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| LIU Chang yu,LI Shi kai and ZHOU Hua ren. Riemann -Stieljes Integral of the Set -valued Stochastic Processes[J]. Journal of PLA University of Science and Technology(Natural Science Edition), 2002, 3(3): 99-102 |
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| Authors: | LIU Chang yu LI Shi kai ZHOU Hua ren |
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| Affiliation: | Institute of Sciences,PLA Univ.of Sci.& Tech.,Nanjing 211101,China;Institute of Sciences,PLA Univ.of Sci.& Tech.,Nanjing 211101,China;Institute of Sciences,PLA Univ.of Sci.& Tech.,Nanjing 211101,China |
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| Abstract: | The integral theory is a new branch of theories of the stochastic processes. In this paper, the Riemann Stieljes integral definition of the set valued stochastic processes is given by means of the similar position and the convergence theory of the random sets. Then its existence criteria is proved. Finally,the integration by parts formula is obtained. These results serve as the theoretical foundation of further research into derivative and integral theories of the set valued stochastic processes. |
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| Keywords: | set valued stochastic processes mean square convergence mean square Riemann Stieljes integral |
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