Extremal statistics for first-passage trajectories of drifted Brownian motion under stochastic resetting

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