论文标题
连续时间多型Ehrenfest模型和相关的Ornstein-uhlenbeck扩散在星形图上
Continuous-time multi-type Ehrenfest model and related Ornstein-Uhlenbeck diffusion on a star graph
论文作者
论文摘要
我们处理通过扩展的星形图定义的连续时间eHrenfest模型，该模型定义为由$ d $ semiaxis的整数形成的晶格。每个光线上的动力学受线性过渡速率调节，而原点的射线之间的切换是根据一般随机矩阵发生的。我们对此过程的瞬态和渐近行为进行详细研究。我们还获得了所考虑模型的扩散近似，这导致了由semiatiatiation形成的域上的ornstein-uhlenbeck扩散过程，该域与原点相连，名为Spider。我们表明，近似过程具有截短的高斯固定密度。最后，通过比较固定分布，均值和方差来讨论近似值的好处。
We deal with a continuous-time Ehrenfest model defined over an extended star graph, defined as a lattice formed by the integers of $d$ semiaxis joined at the origin. The dynamics on each ray are regulated by linear transition rates, whereas the switching among rays at the origin occurs according to a general stochastic matrix. We perform a detailed investigation of the transient and asymptotic behavior of this process. We also obtain a diffusive approximation of the considered model, which leads to an Ornstein-Uhlenbeck diffusion process over a domain formed by semiaxis joined at the origin, named spider. We show that the approximating process possesses a truncated Gaussian stationary density. Finally, the goodness of the approximation is discussed through comparison of stationary distributions, means and variances.
