Distribution of Functionals of Brownian Motion with Linear Drift and Elastically Killed at Zero
摘要
Brownian motion with linear drift on positive half-line and killed elastically at zero is considered. A goal is to get a result that allows us to calculate the distributions of integral functionals with respect to spatial variable of local time of such a process. The explicit form of the distribution of the supremum with respect to spatial variable of local time is calculated for Brownian motion with linear drift reflecting at zero.