Research of dam processes based on the theory of infinitely divisible processes.

基于无限可分过程理论的大坝过程研究

• 批准号: 12640113
• 负责人: INOUE Kazuyuki
• 金额: $ 2.11万
• 依托单位: Shinshu University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2000
• 资助国家: 日本
• 起止时间: 2000 至 2002
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-12640113/
• 关键词: infinitely divisible processes; multiparameter Levy processes; random measures; dam processes; storage processes; Markov chains

We are concerned with venous topics on Levy processes and infinitely divisible processes. The joint work of K. Sato and T. Watanabe clarified the transience levels for Levy processes by using the moments of last exit times. The problem of recurrence-transience for selfsimilar additive processes was discussed in the joint work of Sato and K. Yamamuro. Sato introduced the notion of multiparameter Levy processes with time parameter moving in the positive orthant of a Euclidean space. He studied the hereditary property of selfdecomposability for the multivariate subordination of multiparameter Levy processes. K. Inoue extended the class of multiparameter Levy processes by dropping the time homogenous property of their increments. He described these processes by infinitely divisible random measures and provided the condition for the selfsimilarity. Sato also investigated the relation between cone-parameter Levy processes and convolution semigroups. Inoue introduced a stochastic model for a dam with non-additive and periodic input. He investigated the limiting behavior of the hidden Markov chain when the dam process is characterized by linear release rate function. The nonlinear case was partially solved.

我们关心的静脉主题的Levy过程和无限可分过程。K. Sato和T. Watanabe利用最后退出时刻的矩来阐明Levy过程的瞬变水平。Sato和K.山室Sato引入了多参数Levy过程的概念，其中时间参数在欧氏空间的正正交中移动。他研究了遗传性selfdecomposability的多元从属多参数列维进程。K. Inoue通过去掉多参数Levy过程增量的时间齐次性，推广了多参数Levy过程类。他描述了这些过程的无限可分随机措施，并提供了条件的自相似性。佐藤还研究了锥参数列维过程和卷积半群之间的关系。井上介绍了一个随机模型的大坝与非加性和周期性输入。他研究了极限行为的隐马尔可夫链时，大坝过程的特点是线性释放率函数。非线性问题得到了部分解决。

项目成果

佐藤健一: "Paul Levy "Theorie de l'Addition des Variable Aleatoires"には何が書いてあるか"統計数理研究所 共同研究リポート. 127. 1-14 (2000)

Kenichi Sato：“Paul Levy 的“Theorie de lAddition des Variable Aleatoires”怎么说？” 统计数学研究所联合研究报告 127. 1-14 (2000)。

K.Sato: "Multivariate subordination and selfdecomposability"統計数理研究所 共同研究リポート. 137. 23-28 (2001)

K. Sato：“多元从属性和自分解性”统计数学研究所联合研究报告 137. 23-28 (2001)。

T.Watanabe: "Shift self-similar additive random sequences associated with supercritical branching processes"J. Theoretical Probability. 15(3). 631-665 (2002)

T.Watanabe：“移动与超临界分支过程相关的自相似加性随机序列”J。

T.Watanabe: "Shift selfsimilar random sequences with independent increments"統計数理研究所 共同研究リポート. 127. 61-67 (2000)

T. Watanabe：“以独立增量移位自相似随机序列”统计数学研究所联合研究报告 127. 61-67 (2000)。

真次康夫: "(log^+)pの不変部分空間"数理解析研究所 講究録. 1137. 57-60 (2000)

Yasuo Shinji：“(log^+)p 的不变子空间” Kokyuroku，数学分析研究所，1137. 57-60 (2000)。