隐Brown运动驱动的Poisson过程强度估计量的强相合性

段启宏,陈志平,张改英

系统科学与数学 ›› 2013, Vol. 33 ›› Issue (7) : 751-765.

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系统科学与数学 ›› 2013, Vol. 33 ›› Issue (7) : 751-765. DOI: 10.12341/jssms12128
论文

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
作者信息 +

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

    DUAN Qihong1, CHEN Zhiping2, ZHANG Gaiying3
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文章历史 +

摘要

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.

Abstract

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.

关键词

隐过程 / Poisson 过程 / 强相合性 / 鞅论 / 概率变换.

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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. 系统科学与数学, 2013, 33(7): 751-765. https://doi.org/10.12341/jssms12128
DUAN Qihong, CHEN Zhiping, ZHANG Gaiying. STRONG CONSISTENCY OF ESTIMATORS FOR THE INTENSITY TO A POISSON PROCESS MARKED BY A HIDDEN BROWNIAN PROCESS. Journal of Systems Science and Mathematical Sciences, 2013, 33(7): 751-765 https://doi.org/10.12341/jssms12128
中图分类号: 91B30    60H30   
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