JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2018, Vol. 53 ›› Issue (4): 55-58.doi: 10.6040/j.issn.1671-9352.0.2017.402

Previous Articles     Next Articles

Low order moments of self-excited filtered Poisson processes based on joint distribution of event points

MA Ming, BIAN Li-na*, LIU Hua   

  1. School of Mathematics and Computer Science, Northwest Minzu University, Lanzhou 730030, Gansu, China
  • Received:2017-08-15 Online:2018-04-20 Published:2018-04-13

Abstract: Based on the joint distribution of event points, the first and second order moments of the self-excited shot noise process are given. On this basis, the first and second order moments of Poisson process of self-excited filtering are obtained.

Key words: self-exciting shot noise process, self-exciting filtered Poisson process, customer lifetime value, moment

CLC Number: 

  • O211.6
[1] 马明.自激滤过的泊松过程[J].吉林大学学报(理学版),2009,47(4):711-716. MA Ming. Self-exciting filtered Poisson processes[J]. Journal of Jilin University(Science Edition), 2009, 47(4): 711-716.
[2] 邓永录,梁之舜.随机点过程及其应用[M].北京:科学出版社,1992. DENG Yonglu, LIANG Zhishun. Stochastic point process and its application [M]. Beijing: Science Press, 1992.
[3] 郑莹,马明.自激滤过的泊松过程的二阶矩[J].山东大学学报(理学版),2013,48(9):35-39,45. ZHENG Ying, MA Ming. Second moment of self-exciting filter Poisson process[J].Journal of Shandong University(Natural Science), 2013, 48(9): 35-39, 45.
[4] 樊平毅.随机过程理论与应用[M].北京:清华大学出版社,2005. FAN Pingyi. Stochastic process theory and application[M]. Beijing: Tsinghua University Press, 2005.
[5] 史爱玲,马明,郑莹.齐次泊松响应的客户寿命值及性质[J].山东大学学报(理学版),2014,49(3):96-100. SHI Ailing, MA Ming, ZHENG Ying. Customer lifetime value and property with homogeneous Poisson response [J]. Journal of Shandong University(Natural Science), 2014, 49(3): 96-100.
[6] 马明.δ冲击模型寿命分布的积分计算及M函数的性质[J].山东大学学报(理学版),2008,43(12):15-19. MA Ming. Computation of the integral of lifetime distribution in the δ shock model and the properties of the M function[J].Journal of Shandong University(Natural Science), 2008, 43(12):15-19.
[7] 郑莹,马明. M函数的极限性质[J].经济数学,2014,31(3):92-93. ZHENG Ying, MA Ming. The limit properties of M function[J]. Journal of Quantitative Economics, 2014, 31(3): 92-93.
[8] MA Ming, LI Zehui. Life behavior of censored δ-shock model[J]. Indian Journal of Pure and Applied Mathematics, 2010, 41(2): 401-420.
[1] ZHANG Ya-yun, WU Qun-ying. Precise asymptotics in the law of iterated logarithm for the moment convergence of ρ-mixing sequences [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(4): 13-20.
[2] YANG Chun-hua, CAI Jian-sheng. Classification on f-coloring of graphs with some restrictions [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(2): 37-38.
[3] LI Yong-ming, DENG Shao-jian, JIANG Wei-hong. Consistencies of recursive estimator of a probability density for extended negatively dependent samples [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(11): 54-59.
[4] DENG Xiao-qin, WU Qun-ying. Precise asymptotics in the complete moment convergence for NA random variables [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(1): 102-110.
[5] JIANG Long, CHEN Min. Jensens inequality, moment inequality and law of large numbers for weighted g-expectation [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(8): 1-9.
[6] ZHANG Yu, XIAO Ben-qiong, XU Ke, SHEN Ai-ting. Complete moment convergence for arrays of rowwise NSD random variables [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(6): 30-36.
[7] ZHANG Li-jun, GUO Ming-le. On complete moment convergence of weighted sums for arrays of rowwise asymptotically almost negatively associated random variables [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(2): 42-49.
[8] QIAN Shuo-ge, YANG Wen-zhi. Complete moment convergence of moving average process for END random variables [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2015, 50(06): 13-18.
[9] TAN Chuang, GUO Ming-le, ZHU Dong-jin. Complete moment convergence of weighted sums of arrays of rowwise ND random variables [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2015, 50(06): 27-32.
[10] ZHENG Lu-lu, GE Mei-mei, LIU Yan-fang, WANG Xue-jun. Complete moment convergence for sequences of φ mixing random variables [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2015, 50(04): 14-19.
[11] TIAN You-gong1, JIAO Gui-mei2*. Extremal distribution for the discrete 5-convex stochastic #br# ordering and applications [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2014, 49(1): 99-104.
[12] SHI Ai-ling1, MA Ming2*, ZHENG Ying2. Customer lifetime value and property with #br# homogeneous Poisson response [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2014, 49(03): 96-100.
[13] XU Ri-li, GUO Ming-le*. Complete moment convergence of weighted sums of  arrays of rowwise ND random variables [J]. J4, 2013, 48(6): 9-13.
[14] LI Yong-ming1, DING Li-wang2. The r-th moment consistency of estimators for a semi-parametric regression model for positively associated errors [J]. J4, 2013, 48(1): 83-88.
[15] ZHENG Ying, MA Ming*. Second moment of selfexciting filter poisson process [J]. J4, 2013, 48(09): 35-39.
Viewed
Full text


Abstract

Cited

  Shared   
  Discussed   
No Suggested Reading articles found!