论文标题
加快候选者进程，并进行随机重置
Expediting Feller process with stochastic resetting
论文作者
论文摘要
我们探讨了随机重置对Feller过程的第一步特性的影响。可以将砍伐的过程设想为依赖空间的扩散，而扩散系数$ d（x）= x $，在潜在的$ u（x）= x \ left（\ frac {x} {2} {2}-θ\ right）$中，该$在$θ$中具有最低限度。这将过程限制在起源的积极方面，因此，Feller扩散可以成功地模拟生物学和社会科学中的各种现象，在这种科学中，禁止实现负值。在我们的分析可处理的模型系统中，经历伐木剂扩散的粒子在随机时代后以恒定的速率$ r $恢复为泊松的重置，即将其回到其初始位置。当吸收边界的相对位置（$ x_a $）相对于粒子的初始位置（$ x_0 $）不同时，我们解决了两个不同的情况，即（a）$ x_0 <x_a $和（b）$ x_a <x_0 $。我们观察到，对于$ x_0 <x_a $，当$θ<θ_c$ $θ_c$是$θ_c$的$θ$的临界值时，重置的首次播放加速，当$ x_a $从原点移开时，$θ_c$是$θ$的临界值。与之形成鲜明对比的是，对于$ x_a <x_0 $，当$θ>θ_c$ $θ_c$是$θ_c$的关键值$θ$时，重置的首次通行会加速，当$ x_0 $从原点移开时，它会增加。我们的研究开辟了一系列随后的作品的可能性，并使用重置的更特定于Feller扩散的模型。
We explore the effect of stochastic resetting on the first-passage properties of Feller process. The Feller process can be envisioned as space-dependent diffusion, with diffusion coefficient $D(x)=x$, in a potential $U(x)=x\left(\frac{x}{2}-θ\right)$ that owns a minimum at $θ$. This restricts the process to the positive side of the origin and therefore, Feller diffusion can successfully model a vast array of phenomena in biological and social sciences, where realization of negative values is forbidden. In our analytically tractable model system, a particle that undergoes Feller diffusion is subject to Poissonian resetting, i.e., taken back to its initial position at a constant rate $r$, after random time epochs. We addressed the two distinct cases that arise when the relative position of the absorbing boundary ($x_a$) with respect to the initial position of the particle ($x_0$) differ, i.e., for (a) $x_0<x_a$ and (b) $x_a<x_0$. We observe that for $x_0<x_a$, resetting accelerates first-passage when $θ<θ_c$, where $θ_c$ is a critical value of $θ$ that decreases when $x_a$ is moved away from the origin. In stark contrast, for $x_a<x_0$, resetting accelerates first-passage when $θ>θ_c$, where $θ_c$ is a critical value of $θ$ that increases when $x_0$ is moved away from the origin. Our study opens up the possibility of a series of subsequent works with more case-specific models of Feller diffusion with resetting.
