谱负Lévy过程末离时和占位时的分布研究  

Research on the last exit time and occupation time for spectrally negative Lévy processes

作　　者：陈志颖 CHEN Zhiying(Basic Course Department,Changsha Environmental Protection Vocational College,Changsha 410018,China)

机构地区：[1]长沙环境保护职业技术学院基础课部,湖南长沙410018

出　　处：《湖南文理学院学报(自然科学版)》2025年第1期7-11,共5页Journal of Hunan University of Arts and Science(Science and Technology)

基　　金：国家自然科学基金项目(12271062)。

摘　　要：利用扰动方法和泊松方法研究谱负Lévy过程末离时T_(0)^(+)与首达时τ_(a)^(+)和过程在[0,τ_(a)^(+))上的占位时的联合分布,以及末离时T_(0)^(-)与首达时τ_(a)^(+)和过程在[0,τ_(a)^(+))上的占位时的联合分布。通过对这些分布的深入理解,可以更好地把握谱负Lévy过程的特性,所获得的结果以尺度函数的形式呈现。Using perturbation method and Poisson method,we study the joint distribution of spectrally negative Lévy processes with respect to the last exit time T_(0)^(+),the first exit time τ_(a)^(+) and occupation time of the process over the[0,τ_(a)^(+)),as well as the last exit time T_(0)^(-),the first exit time τ_(a)^(+)and occupation time of the process over the[0,τ_(a)^(+)).By gaining a deeper understanding of these distributions,we can better grasp the characteristics of spectrally negative Lévy processes.The obtained joint Laplace transform can be expressed by the relevant scale function.

关 键 词：谱负Lévy过程 末离时 占位时 联合分布 

分 类 号：O211.6[理学—概率论与数理统计]