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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 first-passage time."
Speaker: Sasi Devan.
Reference: "Julien Randon-Furling and S N Mazumdar."
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 power-law 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.