平稳强相依高斯过程之上穿点过程的极限定理

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平稳强相依高斯过程之上穿点过程的极限定理谭中权嘉兴学院数理信息工程学院, 嘉兴 314001 The Limit Theorems of Upcrossing Point Processes of Stationary Strongly Dependent Gaussian Process TAN Zhong-quanCollege of Mathematics, Physics and Information Engineering, Jiaxing University, Jiaxing 314001, China

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摘要设{X(t)，t≥0}是一列标准化的具有连续样本轨道的强相依平稳高斯过程，其相关系数函数为r(t).当r(t)满足一定条件时，证明了高斯过程{X(t)，t≥0}上穿和ε-上穿水平u形成的点过程的依分布收敛到一Cox-过程.

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收稿日期: 2013-03-01

PACS:

O211.4

基金资助:国家自然科学基金（No.11501250），浙江省自然科学基金（No.Q14A010012，LY15A010019）资助项目.

引用本文:

谭中权. 平稳强相依高斯过程之上穿点过程的极限定理[J]. 应用数学学报, 2016, 39(3): 351-361. TAN Zhong-quan. The Limit Theorems of Upcrossing Point Processes of Stationary Strongly Dependent Gaussian Process. Acta Mathematicae Applicatae Sinica, 2016, 39(3): 351-361.

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