论文标题
重置下的统计波动：严格的结果
Statistical fluctuations under resetting: rigorous results
论文作者
论文摘要
在本文中，我们研究了在一般的非波斯顿重置机制下与随机过程相关的添加功能的正常和大波动。再生过程的累积功能非常接近更新 - 奖励过程，并继承了后者的大多数属性。在这里，我们审查并使用大量的经典定律和中央限制定理进行更新奖励过程，以获得相同的定理，以用于重置的随机过程的加性功能。然后，我们通过说明和应用大型偏差理论来建立这些功能的大偏差原理，以解决作者最近开发的更新奖励过程。我们讨论了一般结果在正职时间，区域和重置布朗运动的绝对区域中的应用。在引入更新理论的高级工具时，我们证明，当人们不仅仅是泊松复位重置时，就会出现一种丰富的现象学对动力学转变的影响。
In this paper we investigate the normal and the large fluctuations of additive functionals associated with a stochastic process under a general non-Poissonian resetting mechanism. Cumulative functionals of regenerative processes are very close to renewal-reward processes and inherit most of the properties of the latter. Here we review and use the classical law of large numbers and central limit theorem for renewal-reward processes to obtain same theorems for additive functionals of a stochastic process under resetting. Then, we establish large deviation principles for these functionals by illustrating and applying a large deviation theory for renewal-reward processes that has been recently developed by the author. We discuss applications of the general results to the positive occupation time, the area, and the absolute area of the reset Brownian motion. While introducing advanced tools from renewal theory, we demonstrate that a rich phenomenology accounting for dynamical phase transitions emerges when one goes beyond Poissonian resetting.
