Two dimensional brownian motion first passage time - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-25T00:52:07Z http://mathoverflow.net/feeds/question/49208 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/49208/two-dimensional-brownian-motion-first-passage-time Two dimensional brownian motion first passage time Lakshmi 2010-12-13T03:46:46Z 2011-02-02T15:22:14Z <p>Hello,</p> <p>I am looking for information on how to solve/compute first passage time for two dimensional Brownian motion.</p> <p>any papers, references, books or web links for study will be helpful. thanks lakshmi</p> http://mathoverflow.net/questions/49208/two-dimensional-brownian-motion-first-passage-time/49212#49212 Answer by nick maxwell for Two dimensional brownian motion first passage time nick maxwell 2010-12-13T04:56:02Z 2010-12-13T04:56:02Z <p>Do you mean this?</p> <p><a href="http://en.wikipedia.org/wiki/First-hitting-time_model" rel="nofollow">http://en.wikipedia.org/wiki/First-hitting-time_model</a></p> <p>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 $E$.</p> <p>-nick</p> http://mathoverflow.net/questions/49208/two-dimensional-brownian-motion-first-passage-time/49247#49247 Answer by Tim van Beek for Two dimensional brownian motion first passage time Tim van Beek 2010-12-13T12:08:28Z 2010-12-13T12:08:28Z <p>Have a look at this page on the Azimuth wiki: <a href="http://www.azimuthproject.org/azimuth/show/First-hitting-time+problem" rel="nofollow">First hitting time problem</a>, there are references and more references on the linked pages.</p> <p>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...</p>