1. Extremal statistics for first-passage trajectories of drifted Brownian motion under stochastic resetting
- Author
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Guo, Wusong, Yan, Hao, and Chen, Hanshuang
- Subjects
Condensed Matter - Statistical Mechanics - Abstract
We study the extreme value statistics of first-passage trajectories generating from a one-dimensional drifted Brownian motion subject to stochastic resetting to the starting point with a constant rate $r$. Each stochastic trajectory starts from a positive position $x_0$ and terminates whenever the particle hits the origin for the first time. \textcolor{blue}{We obtain the exact expression for the marginal distribution $P_r(M|x_0)$ of the maximum displacement $M$}. We find that stochastic resetting has a profound impact on $P_r(M|x_0)$ and the expected value $\langle M \rangle$ of $M$. Depending on the drift velocity $v$, $\langle M \rangle$ shows three distinct trends of change with $r$. For $v \geq 0$, $\langle M \rangle$ decreases monotonically with $r$, and tends to $2x_0$ as $r \to \infty$. For $v_c
v_m$, there is a nonzero resetting rate at which $\langle t_m \rangle$ attains its minimum. Otherwise, $\langle t_m \rangle$ increases monotonically with $r$. We provide an analytical determination of two critical values of $v$, $v_c\approx -1.69415 D/x_0$ and $v_m\approx -1.66102 D/x_0$, where $D$ is the diffusion constant. Finally, numerical simulations are performed to support our theoretical results., Comment: 12 pages, 4 figures. arXiv admin note: substantial text overlap with arXiv:2306.15929; text overlap with arXiv:2307.16443 - Published
- 2023