The approach of Li and Zhou(2014)is adopted to find the Laplace transform of occupation time over interval(0,a)and joint occupation times over semi-infinite intervals(-∞,a)and(b,∞)for a time-homogeneous diffusion pr...The approach of Li and Zhou(2014)is adopted to find the Laplace transform of occupation time over interval(0,a)and joint occupation times over semi-infinite intervals(-∞,a)and(b,∞)for a time-homogeneous diffusion process up to an independent exponential time e_(q)for 0<a<b.The results are expressed in terms of solutions to the differential equations associated with the diffusion generator.Applying these results,we obtain explicit expressions on the Laplace transform of occupation time and joint occupation time for Brownian motion with drift.展开更多
For a < r < b, the approach of Li and Zhou(2014) is adopted to find joint Laplace transforms of occupation times over intervals(a, r) and(r, b) for a time homogeneous diffusion process before it first exits from...For a < r < b, the approach of Li and Zhou(2014) is adopted to find joint Laplace transforms of occupation times over intervals(a, r) and(r, b) for a time homogeneous diffusion process before it first exits from either a or b. 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 on the joint Laplace transforms of occupation times for Brownian motion with drift, Brownian motion with alternating drift and skew Brownian motion, respectively.展开更多
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 ...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 （-∞, a） and （a, ∞）. 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.展开更多
For diffusion processes,we extend various two-sided exit identities to the situation when the process is only observed at arrival times of an independent Poisson process.The results are expressed in terms of solutions...For diffusion processes,we extend various two-sided exit identities to the situation when the process is only observed at arrival times of an independent Poisson process.The results are expressed in terms of solutions to the differential equations associated with the diffusions generators.展开更多
基金Supported by the National Natural Science Foundation of China(12271062,11731012)by the Hunan Provincial National Natural Science Foundation of China(2019JJ50405)。
文摘The approach of Li and Zhou(2014)is adopted to find the Laplace transform of occupation time over interval(0,a)and joint occupation times over semi-infinite intervals(-∞,a)and(b,∞)for a time-homogeneous diffusion process up to an independent exponential time e_(q)for 0<a<b.The results are expressed in terms of solutions to the differential equations associated with the diffusion generator.Applying these results,we obtain explicit expressions on the Laplace transform of occupation time and joint occupation time for Brownian motion with drift.
基金Supported by NSFC(Grant Nos.11171101,11171044,11571052 and 11671132)Key Laboratory of High Performance Computing and Stochastic Information Processing(HPCSIP)+2 种基金Education Ministry of China,Hu’nan Normal UniversityNatural Science Foundation of Hu’nan Province(Grant No.2016JJ4061)Scientific Research Pro ject of Hu’nan University of Arts and Science(Grant No.15ZD05)
文摘For a < r < b, the approach of Li and Zhou(2014) is adopted to find joint Laplace transforms of occupation times over intervals(a, r) and(r, b) for a time homogeneous diffusion process before it first exits from either a or b. 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 on the joint Laplace transforms of occupation times for Brownian motion with drift, Brownian motion with alternating drift and skew Brownian motion, respectively.
文摘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 （-∞, a） and （a, ∞）. 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.
基金This work was supported in part by the National Natural Science Foundation of China(Grant Nos.11571052,11731012)the Natural Science Foundation of Hunan Province(Grant Nos.2018JJ2417,2019JJ50405)+3 种基金the Outstanding Youth Foundation of Hunan Province Department of Education(Grant No.18B401)the China Scholarship Council(Grant No.201808430239)Open Fund of Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering(Grant No.2018MMAEZD02)the Doctoral Scientific Research Project of Hunan University of Arts and Science.
文摘For diffusion processes,we extend various two-sided exit identities to the situation when the process is only observed at arrival times of an independent Poisson process.The results are expressed in terms of solutions to the differential equations associated with the diffusions generators.
