Distribution of the time at which the deviation of a Brownian motion is maximum before its first-passage time - Condensed Matter > Statistical MechanicsReport as inadecuate




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Abstract: We calculate analytically the probability density $Pt m$ of the time $t m$at which a continuous-time Brownian motion with and without drift attains itsmaximum before passing through the origin for the first time. We also computethe joint probability density $PM,t m$ of the maximum $M$ and $t m$. In thedriftless case, we find that $Pt m$ has power-law tails: $Pt m\simt m^{-3-2}$ for large $t m$ and $Pt m\sim t m^{-1-2}$ for small $t m$. Inpresence of a drift towards the origin, $Pt m$ decays exponentially for large$t m$. The results from numerical simulations are in excellent agreement withour analytical predictions.



Author: Julien Randon-Furling LPTMS, Satya N. Majumdar LPTMS

Source: https://arxiv.org/







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