摘要
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.
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.
基金
Supported by NSFC(Grant Nos.11171101,11171044,11571052 and 11671132)
Key Laboratory of High Performance Computing and Stochastic Information Processing(HPCSIP)
Education Ministry of China,Hu’nan Normal University
Natural Science Foundation of Hu’nan Province(Grant No.2016JJ4061)
Scientific Research Pro ject of Hu’nan University of Arts and Science(Grant No.15ZD05)
