Optimal non-Gaussian search with stochastic resetting,Physical Review E

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Optimal non-Gaussian search with stochastic resetting
Physical Review E ( IF 2.2 ) Pub Date : 2021-07-21 , DOI: 10.1103/physreve.104.014125
Aleksander Stanislavsky _{1,

2} , Aleksander Weron ₂

Affiliation

In this paper we reveal that each subordinated Brownian process, leading to subdiffusion, under Poissonian resetting has a stationary state with the Laplace distribution. Its location parameter is defined only by the position to which the particle resets, and its scaling parameter is dependent on the Laplace exponent of the random process directing Brownian motion as a parent process. From the analysis of the scaling parameter the probability density function of the stochastic process, subject to reset, can be restored. In this case the mean time for the particle to reach a target is finite and has a minimum, optimal for the resetting rate. If the Brownian process is replaced by the Lévy motion (superdiffusion), then its stationary state obeys the Linnik distribution which belongs to the class of generalized Laplace distributions.

中文翻译：

具有随机重置的最优非高斯搜索

在本文中，我们揭示了在泊松重置下导致亚扩散的每个从属布朗过程都具有拉普拉斯分布的平稳状态。它的位置参数仅由粒子重置的位置定义，其缩放参数取决于将布朗运动作为父过程的随机过程的拉普拉斯指数。通过对标度参数的分析，可以恢复随机过程的概率密度函数，受重置的影响。在这种情况下，粒子到达目标的平均时间是有限的，并且有一个最小值，即重置率的最佳值。如果布朗过程被 Lévy 运动（超扩散）代替，那么它的静止状态服从属于广义拉普拉斯分布类的 Linnik 分布。

更新日期：2021-07-21

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