A Joint Laplace Transform for Pre-exit Diffusion of Occupation Times

作者：Chen, Ye; Yang, Xiang Qun^*; Li, Ying Qiu; Zhou, Xiao Wen

来源：Acta Mathematica Sinica-English Series, 2017, 33(4): 509-525.

DOI：10.1007/s10114-016-5184-1

• Laplace transform
• occupation time
• time-homogeneous diffusion
• exit time
• Brownian motion with alternating drift
• skew Brownian motion

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.

• 出版日期2017-4
• 单位湖南文理学院; 长沙理工大学; 湖南师范大学