论文标题
通过伽马分布的重置和非传闻回报的扩散过程
Diffusion processes with Gamma-distributed resetting and non-instantaneous returns
论文作者
论文摘要
我们考虑了经过随机重置的布朗粒子的动态演变，这意味着在随机时间段内后，它被迫返回起始位置。之后停止随机运动的间隔是从形状参数$α$和比例参数$ r $的伽马分布中得出的，而返回运动是以恒定速度$ v $进行的，因此，重置的时间与随机阶段中占据的最后一个位置相关。我们表明，对于任何值的$α$，该过程都达到了非平衡稳态，并揭示了固定分布对$ v $的依赖性。有趣的是，稳定状态不受回流速度影响的$α$的单一值。此外，我们通过明确计算平均第一个通道时间来考虑搜索过程的效率。我们所有的发现都通过数值模拟来证实。
We consider the dynamical evolution of a Brownian particle undergoing stochastic resetting, meaning that after random periods of time it is forced to return to the starting position. The intervals after which the random motion is stopped are drawn from a Gamma distribution of shape parameter $α$ and scale parameter $r$, while the return motion is performed at constant velocity $v$, so that the time cost for a reset is correlated to the last position occupied during the stochastic phase. We show that for any value of $α$ the process reaches a non-equilibrium steady state and unveil the dependence of the stationary distribution on $v$. Interestingly, there is a single value of $α$ for which the steady state is unaffected by the return velocity. Furthermore, we consider the efficiency of the search process by computing explicitly the mean first passage time. All our findings are corroborated by numerical simulations.
