An occupation time related potential measure for diffusion processes |
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| Authors: | Ye Chen Yingqiu Li Xiaowen Zhou |
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| Institution: | 1.Hunan Province Cooperative Innovation Center for the Construction and Development of Dongting Lake Ecological Economic Zone and College of Mathematics and Computational Science,Hunan University of Arts and Science,Changde,China;2.School of Mathematics and Statistics,Changsha University of Science and Technology,Changsha,China;3.Department of Mathematics and Statistics,Concordia University,Montreal,Canada |
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| Abstract: | In this paper, for homogeneous diffusion processes, the approach of Y. Li and X. Zhou Statist. Probab. Lett., 2014, 94: 48–55] is adopted to find expressions of potential measures that are discounted by their joint occupation times over semi-infinite intervals (-∞, α) and (α, ∞): 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 for Brownian motion with drift, skew Brownian motion, and Brownian motion with two-valued drift, respectively. |
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