Processes approximating a reflected brownian motion. - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-25T13:59:16Z http://mathoverflow.net/feeds/question/78849 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/78849/processes-approximating-a-reflected-brownian-motion Processes approximating a reflected brownian motion. weakstar 2011-10-22T21:15:32Z 2011-10-23T14:07:54Z <p>Let $W$ be a standard Brownian Motion. Let $\epsilon>0$ be given. Let $X^\epsilon$ be the process which diffuses like $W$ on $(-\epsilon,\infty)$, but when $X^\epsilon$ reaches the level $-\epsilon$, it is immediately brought back to the value zero. It then diffuses again according to $W$ until hitting $-\epsilon$, and then is brought back to zero, and so forth. Let $X^0$ be a reflected Brownian Motion (reflected at zero). Then, as $\epsilon \rightarrow 0$, in what sense does $X^\epsilon \rightarrow X^0$ Are there any references for this? I'm also interested in when $W$ is a diffusion.</p> http://mathoverflow.net/questions/78849/processes-approximating-a-reflected-brownian-motion/78896#78896 Answer by Yuri Bakhtin for Processes approximating a reflected brownian motion. Yuri Bakhtin 2011-10-23T14:07:54Z 2011-10-23T14:07:54Z <p>It looks like it should converge in distribution in Skorokhod space D. Martingale problem approach (see the book by Ethier &amp; Kurtz on Markov processes) should work.</p>