论文标题
具有可变速度和涨幅速度的运行和敲击模型的概率分布
Probability distributions for the run-and-tumble models with variable speed and tumbling rate
论文作者
论文摘要
在本文中，我们考虑了具有时间相关系数的电报方程式，管理粒子在线上持续的随机步行，并以时间变化的速度$ c（t）$移动，并根据非机构Poisson分布分配的速度变化方向，并以速率$λ（t）$。我们表明，在适当的假设下，我们能够找到概率分布的确切形式。我们还考虑了该模型的空间分数对应物，找到了相关过程的特征功能。最终的讨论致力于潜在的应用程序，以进行运行模型。
In this paper we consider a telegraph equation with time-dependent coefficients, governing the persistent random walk of a particle moving on the line with a time-varying velocity $c(t)$ and changing direction at instants distributed according to a non-stationary Poisson distribution with rate $λ(t)$. We show that, under suitable assumptions, we are able to find the exact form of the probability distribution. We also consider the space-fractional counterpart of this model, finding the characteristic function of the related process. A conclusive discussion is devoted to the potential applications to run-and-tumble models.
