Dahlenburg Marcus, Chechkin Aleksei V, Schumer Rina, Metzler Ralf
Institute for Physics & Astronomy, University of Potsdam, 14476 Potsdam, Germany.
Basque Center for Applied Mathematics, 48009 Bilbao, Basque Country, Spain.
Phys Rev E. 2021 May;103(5-1):052123. doi: 10.1103/PhysRevE.103.052123.
Stochastic resetting, a diffusive process whose amplitude is reset to the origin at random times, is a vividly studied strategy to optimize encounter dynamics, e.g., in chemical reactions. Here we generalize the resetting step by introducing a random resetting amplitude such that the diffusing particle may be only partially reset towards the trajectory origin or even overshoot the origin in a resetting step. We introduce different scenarios for the random-amplitude stochastic resetting process and discuss the resulting dynamics. Direct applications are geophysical layering (stratigraphy) and population dynamics or financial markets, as well as generic search processes.
随机重置是一种扩散过程，其幅度在随机时刻被重置为原点，是一种为优化相遇动力学而被深入研究的策略，例如在化学反应中。在这里，我们通过引入随机重置幅度来推广重置步骤，使得扩散粒子在重置步骤中可能仅部分地朝着轨迹原点重置，甚至可能越过原点。我们介绍了随机幅度随机重置过程的不同情形，并讨论了由此产生的动力学。直接应用包括地球物理分层（地层学）、种群动态或金融市场，以及一般的搜索过程。
