Study on Limit Theorems for Random Sets with Dependency

具有相关性的随机集极限定理研究

• 批准号: 14540139
• 负责人: INOUE Hiroshi
• 金额: $ 1.6万
• 依托单位: Tokyo University of Science
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2002
• 资助国家: 日本
• 起止时间: 2002 至 2003
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-14540139/
• 关键词: Random Sets; Law of Large Numbers; Exchangeability; kuratowski-Mosco convergence; Hausdorff Convergence; Dependency; compactness; Fuzzy constraints; ファジィ条件; ファジィランダム集合列

For random sets(or fuzzy random sets) being dependent limit theorems were obtained under the condition that random sets are not compact.Many of the results of laws of large numbers for Banach spaced-value random setswere assumed to be IID(Independent and Identical Distribution) with compactness, and proved by the embedding method and its extension.Moreover, it will be realistic in establishing limit theorems to put some dependency among random sets though IID is, in general, assumed.In this research(1)the author proved strong laws of large numbers for random sets(fuzzy random sets)which posses the nature of dependency, in particular, exchangeability.The topology is based on Kuratowski-Mosco convergence which is weaker than Hausdorff sense and fits into the case of unbounded random sets with more applicable nature.(2)One algorithm to solve convex maximization problem was established with fuzzy constraints.The objective function of encountered problem is convex and its feasible region is inverse convex. In the future work, it is expected to establish algorithms of maximization problems by introducing random sets concept with stochastic process of fuzzy nature.

对于随机集在随机集不紧的条件下，得到了Banach空间值随机集（或模糊随机集）的相依极限定理，并将Banach空间值随机集的大数定律的许多结果假定为IID（独立同分布）的一个新的性质，并利用嵌入方法及其推广得到了证明，同时，在建立极限定理时，尽管IID通常是，在本研究中（1）证明了随机集的强大数定律该拓扑结构基于Kuratowski-Mosco收敛，比Hausdorff意义弱，适用于无界随机集的情形，具有更强的适用性。（2）建立了一种求解带模糊约束的凸极大化问题的算法，所遇到的问题的目标函数是凸的，其可行域是反凸的。在未来的工作中，我们期望通过引入随机集的概念，建立模糊随机过程的最大化问题的算法。

项目成果

Hiroshi Inoue: "Laws of Large Numbers for Exchangeable Random Sets in Kuratowski-Mosco Sense"Stochastic Analysis and Applications. (revised).

Hiroshi Inoue：“Kuratowski-Mosco Sense 中可交换随机集的大数定律”随机分析和应用。

Jianming shi, Hiroshi Inoue: "Convex Maximization on a Convex Set with Fuzzy Constraints"IEEE Transaction on Systems, Man and Cybernetics, PART A. (Accepted).

石建明，Hiroshi Inoue：“具有模糊约束的凸集上的凸最大化”IEEE Transaction on Systems, Man and Cyber​​netics, PART A.（已接受）。

Hiroshi Inoue: "Laws of large Numbers for Exchangeable Random Sets in Kuratowski-Mosco Sense"Stochastic Analysis and Applications. (revised 中).

Hiroshi Inoue：“Kuratowski-Mosco Sense 中可交换随机集的大数定律”随机分析和应用（当前修订）。

Jianming Shi: "Convex Maximization on a Convex Set with Fuzzy Constraints"IEEE Transaction on Systems, Man and Cybernetics, Part A. (印刷中).

施建明：“具有模糊约束的凸集上的凸最大化”IEEE Transaction on Systems, Man and Cyber​​netics, Part A.（出版中）。

Hiroshi Inoue: "Laws of Large Numbers for Exchangeable Random Sets in Kuratowski-Mosco Sense"Stochastic Analysis and Applications. (revised中).

Hiroshi Inoue：“Kuratowski-Mosco Sense 中可交换随机集的大数定律”随机分析和应用（修订版）。