Diffusion occupation time before exiting  

作　　者：Yingqiu LI Suxin WANG Xiaowen ZHOU Na ZHU 

机构地区：[1]College of Mathematics and Computing Sciences, Changsha University of Science and Technology, Changsha 410004, China [2]College of Mathematics, Nankai University, Tianjin 300071, China [3]Department of Mathematics and Statistics, Concordia University, Montreal,Quebec H3G 1M8, Canada

出　　处：《Frontiers of Mathematics in China》2014年第4期843-861,共19页中国高等学校学术文摘·数学（英文）

基　　金：Acknowledgements The authors thank the anonymous referees for helpful comments. Yingqiu Li＇s work was supported by the National Natural Science Foundation of China （Grant No. 11171044） und the Natural Science Foundation of Hunan Province （Grant No. llJ32001）; Suxin Wang＇s work was supported by the Natural Sciences and Engineering Research Council of Canada.

摘　　要：Using the approach of D. Landriault et al. and B. Li and X. Zhou, for a one-dimensional time-homogeneous diffusion process X and constants c 〈 a 〈 b 〈 d, we find expressions of double Laplace transforms of the form Ex[e--θTd--λ∫o Td1a 〈Xs〈b ds; Td 〈 Tc], where Tx denotes the first passage time of level x. As applications, we find explicit Laplace transforms of the corresponding occupation time and occupation density for the Brownian motion with two-valued drift and that of occupation time for the skew Ornstein- Uhlenbeck process, respectively. Some known results are also recovered.Using the approach of D. Landriault et al. and B. Li and X. Zhou, for a one-dimensional time-homogeneous diffusion process X and constants c 〈 a 〈 b 〈 d, we find expressions of double Laplace transforms of the form Ex[e--θTd--λ∫o Td1a 〈Xs〈b ds; Td 〈 Tc], where Tx denotes the first passage time of level x. As applications, we find explicit Laplace transforms of the corresponding occupation time and occupation density for the Brownian motion with two-valued drift and that of occupation time for the skew Ornstein- Uhlenbeck process, respectively. Some known results are also recovered.

关 键 词：DIFFUSION exit problem occupation time occupation density localtime Brownian motion with two-valued drift skew Ornstein-Uhlenbeck （OU）process 

分 类 号：O211.6[理学—概率论与数理统计] TN241[理学—数学]