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
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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...