Condensed Matter and Statistical Physics Journal Club
Date:  Aug 03, 2009 
Title: 
"Distribution of the time at which the deviation of a Brownian motion is maximum before its firstpassage time." 

Speaker: 
Sasi Devan. 

Reference: 
"Julien RandonFurling and S N Mazumdar.http://iopscience.iop.org/17425468/2007/10/P10008/pdf/17425468_2007_10_P10008.pdf" 
Abstract: 
We calculate analytically the probability density p(tm ) of the time tm at which a continuous – time Brownian motion (with and without drift ) attains its maximum before passing through the origin for the first time. We also compute the joint probability density P(M, tm) of the maximum M and tm.In the drift less case, we find that P( tm) has powerlaw tails. P( tm) ~ tm 3/2 for large tm and P( tm) ~ tm 1/2 for small tm . In the presence of a drift towards the origin, P( tm) decays exponentially for large tm . The results from numerical simulations are in excellent agreement with our analytical predictions.
