兰州大学机构库 >数学与统计学院
基于簇生标值点过程的冲击模型及其应用
Alternative TitleShock Models Based on A Marked Cluster Point Process and Their Applications
白建明
Thesis Advisor李泽慧
2008-05-28
Degree Grantor兰州大学
Place of Conferral兰州
Degree Name博士
Keyword冲击模型 簇生标值点过程 系统寿命 正则尾分布 无穷可分分布 保险风险模型 失效(破产) 概率
Abstract冲击模型是可靠性理论的主要分支之一,是描述随机环境下工作的系统的寿命性质的有效工具。冲击模型的研究涉及随机过程、极限理论的思想与方法,并涉及到随机变量的随机和、最大值等经典问题,具有重要的理论价值。应用则涉及科学技术与社会经济的许多领域,如网络、机电、生产、存储、金融与保险、管理、生态、交通、军事等系统以及许多自然现象。簇生标值点过程是定义在某概率空间上的随机过程,是主过程和附加过程族的叠加。一些重要的簇生点过程包括Neyman-Scott模型、Bartlett-Lewis模型及其各种变形。Daley等 (2003,174页)指出,簇生点过程不仅是理论上十分重要的一类随机过程,同时也是描述一大类复杂的自然和社会现象的天然工具。本文基于簇生标值点过程框架对传统冲击模型进行推广,讨论推广冲击模型的一系列性质,包括寿命性质和极限行为,并探索推广模型在保险风险理论中的应用。这样的推广,本质上将经典的随机变量的随机和问题提升至随机过程的随机和的研究水平,并使模型能够描述一大类复杂系统。
Other AbstractShock models, one of the important branches of reliability, are the powerful tools to describe the lifetime behavior of a system operating in random environment. The study of shock models relates remarkably to stochastic processes and limit theory, also involves in some classical mathematical topics such as random sum and maximum of random variables. The applications cover the fields of engineering, technology and economics, including network safety, mechanical/electronic engineering, production/inventory, finance, insurance, management, ecosystem, transportation and some natural phenomena. A marked cluster point process is a stochastic process defined on some probability space, it is a superposition of the primary process and the adjunct processes. Several influential cluster point processes are Neyman-Scott model, Bartlett-Lewis model and their transformations. As Daley D.J. et al. (2003, P174) said: Cluster processes form one of the most important and widely used models in point process studies, whether applied or theoretical, they are natural models for the locations of objects in the plane or in three-dimensional space.The main aim of the present dissertation is to generalize the traditional shock models based on a framework of marked cluster processes, to investigate lifetime characteristics and limit behaviors of the extended shock model, and then to attempt their applications in insurance risk. The essential significance of such a generalization is to advance the classical random sum of random variables into the random sum of stochastic processes, also to adapt shock models to a wider reliability field.
URL查看原文
Language中文
Document Type学位论文
Identifierhttps://ir.lzu.edu.cn/handle/262010/225188
Collection数学与统计学院
Recommended Citation
GB/T 7714
白建明. 基于簇生标值点过程的冲击模型及其应用[D]. 兰州. 兰州大学,2008.
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