[Math] Two dimensional brownian motion first passage time

Question

Hello,

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

Answer 1

Do you mean this?

http://en.wikipedia.org/wiki/First-hitting-time_model

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 $E$.

-nick