一维时齐带反射边界零常返扩散过程回返时的矩  

Return time moment of time-homogeneous and null-recurrent one-dimension diffusion with reflection boundary

作　　者：王颖喆[1] 郑家森 郝一菲 WANG Yingzhe;ZHENG Jiasen;HAO Yifei(School of Mathematical Sciences,Key Laboratory of Mathematics and Complex Systems of Ministry of Education,Beijing Normal University,Beijing,China)

机构地区：[1]北京师范大学数学科学学院,数学与复杂系统教育部重点实验室,北京

出　　处：《北京师范大学学报（自然科学版）》2024年第4期461-467,共7页Journal of Beijing Normal University(Natural Science)

基　　金：国家自然科学基金资助项目(11871103)。

摘　　要：基于半直线[0,∞)带反射边界的一维时齐零常返扩散过程,探讨了其击中固定点1后首次回返时的矩,并对回返时Laplace变换所满足的带反射边界条件微分方程的近似解进行了估计;由Tauberian引理获得了回返时概率分布的渐近估计,并得到了回返时的γ阶矩有限时,阶数γ的取值范围.This work aims to study moment of return time of time-homogeneous and null-recurrent onedimension diffusion on[0,∞)with reflection boundary,to solve estimation of approximate solution of differential equation with reflection boundary satisfied by the Laplace transform in return time.Asymptotic estimation of probability distribution in return time is obtained using Tauberian lemma.When γ-moment is finite the range of order γ is calculated.

关 键 词：扩散过程 回返时的矩 零常返 反射边界 LAPLACE变换 

分 类 号：O211.62[理学—概率论与数理统计] O211.63[理学—数学]