Frontiers of Mathematics in China >
Diffusion occupation time before exiting
Received date: 19 Feb 2014
Accepted date: 17 Jun 2014
Published date: 20 Aug 2014
Copyright
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 , 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.
Yingqiu LI , Suxin WANG , Xiaowen ZHOU , Na ZHU . Diffusion occupation time before exiting[J]. Frontiers of Mathematics in China, 2014 , 9(4) : 843 -861 . DOI: 10.1007/s11464-014-0402-6
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