Montero Miquel, Palassini Matteo, Masoliver Jaume
Department of Condensed Matter Physics and Institute of Complex Systems (UBICS), <a href="https://ror.org/021018s57">University of Barcelona</a>, Catalonia 08028, Spain.
Phys Rev E. 2024 Jul;110(1-1):014116. doi: 10.1103/PhysRevE.110.014116.
We study the counting of level crossings for inertial random processes exposed to stochastic resetting events. We develop the general approach of stochastic resetting for inertial processes with sudden changes in the state characterized by position and velocity. We obtain the level-crossing intensity in terms of that of underlying reset-free process for resetting events with Poissonian statistics. We apply this result to the random acceleration process and the inertial Brownian motion. In both cases, we show that there is an optimal resetting rate that maximizes the crossing intensity, and we obtain the asymptotic behavior of the crossing intensity for large and small resetting rates. Finally, we discuss the stationary distribution and the mean first-arrival time in the presence of resettings.
我们研究了暴露于随机重置事件的惯性随机过程的能级交叉计数。我们为具有以位置和速度为特征的状态突然变化的惯性过程开发了随机重置的一般方法。对于具有泊松统计的重置事件，我们根据基础无重置过程的能级交叉强度得出了能级交叉强度。我们将此结果应用于随机加速过程和惯性布朗运动。在这两种情况下，我们都表明存在一个最优重置率，可使交叉强度最大化，并且我们得出了大小重置率下交叉强度的渐近行为。最后，我们讨论了存在重置时的平稳分布和平均首次到达时间。
