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...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.展开更多
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.
文摘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.
