Diffusion occupation time before exiting

作     者：Yingqiu LI Suxin WANG Xiaowen ZHOU Na ZHU 

作者机构：College of Mathematics and Computing Sciences Changsha University of Science and Technology Changsha 410004 China College of Mathematics Nankai University Tianjin 300071 China Department of Mathematics and Statistics Concordia University MontrealQuebec H3G 1M8 Canada 

出 版 物：《Frontiers of Mathematics in China》 (中国高等学校学术文摘·数学（英文）)

年 卷 期：2014年第9卷第4期

页      面：843-861页

核心收录：

学科分类：02[经济学] 0202[经济学-应用经济学] 020208[经济学-统计学] 070207[理学-光学] 07[理学] 0714[理学-统计学（可授理学、经济学学位）] 070103[理学-概率论与数理统计] 0701[理学-数学] 0702[理学-物理学] 

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 

主　　题：Diffusion exit problem occupation time occupation density localtime Brownian motion with two-valued drift skew Ornstein-Uhlenbeck (OU)process 

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.