• 论文 •    下一篇

隐Brown运动驱动的Poisson过程强度估计量的强相合性

段启宏1,陈志平2,张改英3   

  1. 1. 西安交通大学数学与统计学院 统计系,西安 710049; 2. 西安交通大学数学与统计学院 计算科学系,西安, 710049; 3. 西安交通大学数学与统计学院 统计系, 西安 710049
  • 收稿日期:2011-06-01 出版日期:2013-07-25 发布日期:2013-09-18

段启宏,陈志平,张改英. 隐Brown运动驱动的Poisson过程强度估计量的强相合性[J]. 系统科学与数学, 2013, 33(7): 751-765.

DUAN Qihong, CHEN Zhiping, ZHANG Gaiying. STRONG CONSISTENCY OF ESTIMATORS FOR THE INTENSITY TO A POISSON PROCESS MARKED BY A HIDDEN BROWNIAN PROCESS[J]. Journal of Systems Science and Mathematical Sciences, 2013, 33(7): 751-765.

STRONG CONSISTENCY OF ESTIMATORS FOR THE INTENSITY TO A POISSON PROCESS MARKED BY A HIDDEN BROWNIAN PROCESS

DUAN Qihong1, CHEN Zhiping2, ZHANG Gaiying3   

  1. 1. Department of Statistics, School of Mathematics and Statistics, Xi’an Jiaotong University,Xi’an 710049; 2.Department of Computing Science, School of Mathematics and Statistics,Xi’an Jiaotong University, Xi’an 710049; 3.Department of Statistics, School of Mathematics and Statistics,Xi’an Jiaotong University, Xi’an 710049
  • Received:2011-06-01 Online:2013-07-25 Published:2013-09-18
针对金融、保险等领域研究中经常遇到的隐Brown运动驱动的Poisson过程模型, 通过概率变换并利用鞅论方法等工具, 证明了对模型中某些参数所提出的两类估计量的强相合性, 用数值试验检验了它们的有效性. 试验结果表明,  文中所给两类估计方法均优于已有方法.
For a kind of hidden Brownian marked Poisson processes arising from the finance and insurance field, it is proved that two types of proposed estimators are
stronconsistent by using the martingale theory and the reference probability mea- sures. Efficiency of designed estimators are examined through numerical experiments and are also compared with current estimators. Numerical results show that the new estimatrs are superior to the existing estimators.

MR(2010)主题分类: 

()
[1] 乔克林,韩建勤. 改进后的复合~Poisson-Geometric 风险模型~Gerber-Shiu 折现惩罚函数[J]. 系统科学与数学, 2016, 36(10): 1743-1752.
[2] 周兴才;胡舒合. NA样本部分线性模型估计的强相合性[J]. 系统科学与数学, 2010, 30(1): 60-071.
[3] 朱复康;王德辉. 一个简化的新Laplace AR(1)模型 参数估计及其渐近性质[J]. 系统科学与数学, 2009, 29(1): 129-135.
[4] 肖丽华. NA样本线性回归参数的M估计的强相合性[J]. 系统科学与数学, 2007, 27(2): 255-264.
[5] 崔恒建. 变系数线性EV模型参数的调整加权最小二乘估计及其渐近性质[J]. 系统科学与数学, 2007, 27(1): 82-92.
[6] 陈家骅;李鹏飞;谭鲜明. 混合von Mises 模型的参数估计[J]. 系统科学与数学, 2007, 27(1): 59-67.
[7] 陈敏. 平稳MA模型阶数的Bayesian估计[J]. 系统科学与数学, 1998, 18(4): 447-454.
[8] 张所地;范金城. AR(1)-MA(0)模型的参数矩估计及其优良性质[J]. 系统科学与数学, 1995, 15(2): 97-106.
阅读次数
全文


摘要