论文标题
死亡率对重置随机搜索过程的影响
Effects of mortality on stochastic search processes with resetting
论文作者
论文摘要
我们研究了凡人布朗粒子的起源的第一分时间，死亡率$μ$，在一个维度上扩散。粒子从$ x> 0 $开始运动，并通过恒定速率$ r $进行随机重置。我们首先公布了在没有死亡率的情况下达到目标问题的概率与相应问题的平均第一通道时间之间的关系，这使我们能够根据哪些条件来通过调整重新启动率来提高前者的条件。然后，我们将粒子在死亡之前达到目标的事件的条件下，将均值和方差的精确表达式视为$ r $的函数，并通过数值模拟证实。通过研究重置对不同死亡率制度的影响，我们还表明，如果平均生命周期$τ_μ= 1/μ$相对于扩散的时间尺度$τ_d= x^2/（4D）$，则存在两个重新确定$r_μ^* $最大化的可能性和最大值$ r_m $ r_m $ r_m的均值。但是，两者从不重合正$μ$，这使得优化问题高度不平凡。
We study the first-passage time to the origin of a mortal Brownian particle, with mortality rate $ μ$, diffusing in one dimension. The particle starts its motion from $ x>0 $ and it is subject to stochastic resetting with constant rate $ r $. We first unveil the relation between the probability of reaching the target and the mean first-passage time of the corresponding problem in absence of mortality, which allows us to deduce under which conditions the former can be increased by adjusting the restart rate. We then consider the first-passage time conditioned on the event that the particle reaches the target before dying, and provide exact expressions for the mean and the variance as functions of $ r $, corroborated by numerical simulations. By studying the impact of resetting for different mortality regimes, we also show that, if the average lifetime $ τ_μ=1/μ$ is long enough with respect to the diffusive time scale $ τ_D=x^2/(4D) $, there exist both a resetting rate $ r_μ^* $ that maximizes the probability and a rate $ r_m $ that minimizes the mean first-passage time. However, the two never coincide for positive $ μ$, making the optimization problem highly nontrivial.
