| 一类广义复合Poisson过程 |
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| 引用本文： | 方世祖,孙歆.一类广义复合Poisson过程[J].纯粹数学与应用数学,2009,25(1). |
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| 作者姓名： | 方世祖 孙歆 |
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| 作者单位： | 1. 西安交通大学理学院,陕西,西安,710049;广西大学数学与信息科学学院,广西,南宁,530004
2. 广西大学数学与信息科学学院,广西,南宁,530004 |
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| 摘 要： | 给出广义复合Poisson过程的定义,讨论它的基本性质和强马氏性,在假定个体分布是亚指数分布的条件下,给出它的一维分布函数的尾等价公式.证明任意多个相互独立的广义复合Poisson过程的线性组合是一个复合Poisson过程.
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| 关 键 词： | 平稳无后效流 复合Poisson过程 强马氏性 线性组合 矩母函数 亚指数分布 |
A class of generalized compound Poisson process |
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| FANG Shi-zu,SUN Xin.A class of generalized compound Poisson process[J].Pure and Applied Mathematics,2009,25(1). |
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| Authors: | FANG Shi-zu SUN Xin |
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| Institution: | FANG Shi-zu1,2,SUN Xin2 |
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| Abstract: | A generalized compound Poisson process is defined. Its some elementary properties and strongly Markov property are discussed. Under the assumption that the individual distribution function is subexponential,a tail asymptotic relationship of its one-dimensional distribution function is established. It is showed that a linear combination with independently generalized compound Poisson processes is a compound Poisson process. |
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| Keywords: | stationary stream of random events with independent increments compound Poisson process strongly Markov property linear combination moment generating function subexponential distributions |
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