In the classical stochastic resetting problem, a particle, moving according to some stochastic dynamics, undergoes random interruptions that bring it to a selected domain, and then the process recommences. Hitherto, the resetting mechanism has been introduced as a symmetric reset about the preferred location. However, in nature, there are several instances where a system can only reset from certain directions, e.g., catastrophic events. Motivated by this, we consider a continuous stochastic process on the positive real line. The process is interrupted at random times occurring at a constant rate, and then the former relocates to a value only if the current one exceeds a threshold; otherwise, it follows the trajectory defined by the underlying process without resetting. An approach to obtain the exact nonequilibrium steady state of such systems and the mean first passage time to reach the origin is presented. Furthermore, we obtain the explicit solutions for two different model systems. Some of the classical results found in symmetric resetting, such as the existence of an optimal resetting, are strongly modified. Finally, numerical simulations have been performed to verify the analytical findings, showing an excellent agreement.

中文翻译：

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非对称随机重置：灾难性事件建模

在经典的随机重置问题中，根据某些随机动力学运动的粒子会经历随机中断，将其带到选定的域，然后过程重新开始。迄今为止，已经将复位机制作为关于优选位置的对称复位而引入。但是，实际上，在某些情况下，系统只能从某些方向重置，例如灾难性事件。因此，我们考虑了正实线上的连续随机过程。该过程在以恒定速率发生的随机时间中断，然后仅当当前阈值超过阈值时，前者才会重新定位为某个值；否则，它将遵循基础流程定义的轨迹，而无需重置。提出了一种获取此类系统确切的非平衡稳态以及到达原点的平均第一次通过时间的方法。此外，我们获得了两个不同模型系统的显式解。对称重设中发现的一些经典结果（例如，最优重设的存在）被强烈修改。最后，进行了数值模拟以验证分析结果，显示出极好的一致性。