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
$\begingroup$
$\endgroup$
Add a comment
|
2 Answers
$\begingroup$
$\endgroup$
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
$\begingroup$
$\endgroup$
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...
