Hi everybody


Let $U$ be the domain (as shown in the picture) and $\bar{U}$ its closure, further more set $\partial\_r U$ to be the reflecting boundary and $\partial\_a U$ the absorbing one. The process $(X\_t)\_{t\geq 0}$ is chosen as described above and $\tau=\inf(t\geq 0, X\_t \in \partial\_a U)$ is the first hitting time of the absorbing boundary. 


Thanks in advance - any kind of advice would be great :)



Continuity of hitting distributions
How about transforming the corner conformally into a part of a line? The process would transform into a time-changed Brownian motion, again with normal reflection (since the map is conformal up to the boundary, with the only exception at that corner point, and I guess the process never hits that point). And then use the same argument with convergence of hitting distribution.


