延迟随机游动的超出的局部渐近性质
The Local Asymptotics of the Overshoot of a Delay Random Walk
DOI: 10.12677/SA.2019.82041, PDF,    科研立项经费支持
作者: 胡甜甜*, 吉正敏, 毛砚竹*, 王开永*：苏州科技大学数理学院，江苏 苏州
关键词: 随机游动；延迟；超出；局部渐近性质； Random Walk； Delay； Overshoot； Local Asymptotics
摘要: 本文讨论带有延迟的随机游动，利用建立的更新方程，借助零延迟的结果，在随机游动增量的分布具有重尾情形下，得到了延迟随机游动超出的局部渐近性质。 This paper investigates a delay random walk. Using the renewal equation and the results of random walk with zero delay, when the distribution of the increment of the random walk has a heavy tail, the paper obtains the local asymptotics of the overshoot of the delay random walk.
文章引用：胡甜甜, 吉正敏, 毛砚竹, 王开永. 延迟随机游动的超出的局部渐近性质[J]. 统计学与应用, 2019, 8(2): 370-374. https://doi.org/10.12677/SA.2019.82041

参考文献

[1] Janson, S. (1986) Moments for First-Passage and Last-Exit Times, the Minimum, and Related Quantities for Random Walks with Positive Drift. Advances in Applied Probability, 18, 865-879. [Google Scholar] [CrossRef] 
[2] Borovkov, A.A. and Foss, S. (2000) Estimates for Overshooting an Arbi-trary Boundary by a Random Walk and Their Applications. Theory of Probability & Its Applications, 44, 231-253. [Google Scholar] [CrossRef] 
[3] Klüppelberg, C., Kyprianou, A.E. and Maller, R.A. (2004) Ruin Probabilities and Overshoots for General Lévy Insurance Risk Process. The Annals of Applied Probability, 14, 1766-1801. [Google Scholar] [CrossRef] 
[4] Tang, Q. (2007) The Overshoot of a Random Walk with Negative Drift. Statistics & Probability Letters, 77, 158-165. [Google Scholar] [CrossRef] 
[5] Chen, G., Wang, Y. and Cheng, F. (2009) The Uniform Local Asymptotics of the Overshoot of a Random Walk with Heavy-Tailed Increments. Stochastic Models, 25, 508-521. [Google Scholar] [CrossRef] 
[6] Cui, Z., Wang, Y. and Wang, K. (2009) Asymptotics for the Moments of the Overshoot and Undershoot of a Random Walk. Advances in Applied Probability, 41, 469-494. [Google Scholar] [CrossRef] 
[7] Klüppelberg, C. (1989) Subexponential Distributions and Charac-terizations of Related Classes. Probability Theory and Related Fields, 82, 259-269. [Google Scholar] [CrossRef] 
[8] Cline, D.B.H. and Samorodnitsky, G. (1994) Subexponentiality of the Product of Independent Random Variables. Stochastic Processes and their Applications, 49, 75-98. [Google Scholar] [CrossRef] 
[9] Klüppelberg, C. (1988) Subexponential Distributions and In-tegrated Tails. Journal of Applied Probability, 25, 132-141. [Google Scholar] [CrossRef] 
[10] Embrechts, P., Klüppelberg, C. and Mikosch, T. (1997) Mod-elling Extremal Events. Springer, Berlin. [Google Scholar] [CrossRef] 
[11] Gao, Q. and Wang, Y. (2009) Ruin Probability and Local Ruin Probability in the Random Multi-Delayed Renewal Risk Model. Statistics & Probability Letters, 79, 588-596. [Google Scholar] [CrossRef] 

为你推荐