I am looking for information on how to solve/compute first passage time for two dimensional Brownian motion.
any papers, references, books or web links for study will be helpful. thanks lakshmi
Do you mean this?
I've always just run the sample path (so, a loop which cumulatively sums $dX(t)$) until some condition is met, then end the loop, returing $t$ and $X(t)$. I guess your condition would be $X(t) \in E$, for some borel set $E$.
Have a look at this page on the Azimuth wiki: First hitting time problem, there are references and more references on the linked pages.
The solution of the one-dimensional diffusion process that is absorbed at two boundary points, which is explained on that page, can be generalized to more dimensions...