论文标题
电报随机演变圈子
Telegraph random evolutions on a circle
论文作者
论文摘要
我们考虑通过在圆上移动的粒子的运动来描述的随机演变，交替的角度速度$ \ pm c $并在泊松随机时间上改变旋转，从而在圆上产生了电报过程。我们研究了其产生的半群的分析特性及其概率分布。还研究了包装过程的渐近行为，以圆形的布朗运动。此外，有可能为谐波振荡器的随机变化而得出随机变化的随机模型，并且我们给出了该过程的扩散近似值。此外，我们在不对称的情况下以及非马克维亚的等待时间中介绍了圆形电报模型的一些扩展。在最后一个情况下，我们还提供了一些渐近考虑因素。
We consider the random evolution described by the motion of a particle moving on a circle alternating the angular velocities $ \pm c $ and changing rotation at Poisson random times, resulting in a telegraph process over the circle. We study the analytic properties of the semigroup it generates as well as its probability distribution. The asymptotic behavior of the wrapped process is also studied in terms of circular Brownian motion. Besides, it is possible to derive a stochastic model for harmonic oscillators with random changes in direction and we give a diffusive approximation of this process. Furthermore, we introduce some extensions of the circular telegraph model in the asymmetric case and for non-Markovian waiting times as well. In this last case, we also provide some asymptotic considerations.
