| 以分数布朗运动为输入过程的存储过程生成的上穿点过程 |
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| 引用本文： | 马芳丽,谭中权. 以分数布朗运动为输入过程的存储过程生成的上穿点过程[J]. 数学进展, 2020, 0(2): 241-252 |
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| 作者姓名： | 马芳丽 谭中权 |
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| 作者单位： | 嘉兴学院数理与信息工程学院 |
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| 基金项目： | Supported by NSFC(No.11501250);Natural Science Foundation of Zhejiang Province of China(No.LY18A010020);Xinmiao Talents Project of Zhejiang Province of China(No.2019R417013);SRT of Jiaxing University(No.851719603)。 |
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| 摘 要： | 本文研究了以分数布朗运动为输入过程的存储过程上穿高水平u形成的点过程的渐近泊松特性,结果表明当分数布朗运动参数H∈(0,1/2),u→∞时,该点过程弱收敛到泊松过程.
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| 关 键 词： | 点过程 上穿 存储过程 分数布朗运 |
The Point Process of Upcrossings Formed by Storage Process with Fractional Brownian Motion as Input |
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| MA Fangli,TAN Zhongquan. The Point Process of Upcrossings Formed by Storage Process with Fractional Brownian Motion as Input[J]. Advances in Mathematics(China), 2020, 0(2): 241-252 |
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| Authors: | MA Fangli TAN Zhongquan |
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| Affiliation: | (College of Mathematics,Physics and Information Engineering,Jioxing University,Jiaxing,Zhejiang,314001,P.R.China) |
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| Abstract: | In this paper,the asymptotic Poisson character of the point process formed by the upcrossings of increasingly high levels u by the so-called storage process with fractional Brownian motion as input is studied.It is shown that the point process converges weakly to a Poisson process N as u→∞,when the Hurst parameter H of the fractional Brownian motion belongs to(0,1/2). |
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| Keywords: | point process upcrossings storage process fractional Brownian motion |
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