A Joint Laplace Transform for Pre-exit Diffusion of Occupation Times  

作　　者：Ye CHEN Xiang Qun YANG Ying Qiu LI Xiao Wen ZHOU 

机构地区：[1]College of Mathematics and Computer Science, Hu'nan Normal University [2]College of Mathematics and Computational Science, Hu’nan University of Arts and Science [3]College of Mathematics and Statistics, Changsha University of Science and Technology [4]Department of Mathematics and Statistics, Concordia University

出　　处：《Acta Mathematica Sinica,English Series》2017年第4期509-525,共17页数学学报（英文版）

基　　金：Supported by NSFC(Grant Nos.11171101,11171044,11571052 and 11671132);Key Laboratory of High Performance Computing and Stochastic Information Processing(HPCSIP);Education Ministry of China,Hu’nan Normal University;Natural Science Foundation of Hu’nan Province(Grant No.2016JJ4061);Scientific Research Pro ject of Hu’nan University of Arts and Science(Grant No.15ZD05)

摘　　要：For a < r < b, the approach of Li and Zhou(2014) is adopted to find joint Laplace transforms of occupation times over intervals(a, r) and(r, b) for a time homogeneous diffusion process before it first exits from either a or b. The results are expressed in terms of solutions to the differential equations associated with the diffusions generator. Applying these results, we obtain more explicit expressions on the joint Laplace transforms of occupation times for Brownian motion with drift, Brownian motion with alternating drift and skew Brownian motion, respectively.For a < r < b, the approach of Li and Zhou(2014) is adopted to find joint Laplace transforms of occupation times over intervals(a, r) and(r, b) for a time homogeneous diffusion process before it first exits from either a or b. The results are expressed in terms of solutions to the differential equations associated with the diffusions generator. Applying these results, we obtain more explicit expressions on the joint Laplace transforms of occupation times for Brownian motion with drift, Brownian motion with alternating drift and skew Brownian motion, respectively.

关 键 词：Laplace transform occupation time time-homogeneous diffusion exit time Brownian motion with alternating drift skew Brownian motion 

分 类 号：O211.6[理学—概率论与数理统计]