论文标题
订购的指数随机步行
Ordered exponential random walks
论文作者
论文摘要
我们研究了$ d $维的随机步行，并具有指数分布的增量条件，以便组件保持有序（从DOOB的意义上）。我们发现，杀死过程明确发现了一个正谐波功能$ h $，然后使用DOOB的$ H $转换来构建一个有序的过程。由于这些随机步行不是最近的邻居，因此谐波功能不是Vandermonde的决定因素。有序过程与同时的M/M/1队列的出发过程有关。我们发现，直到指数随机步行中的组成部分变得无序和局部极限定理，渐近概率为止。我们发现最小和最大颗粒的过程的分布是弗雷德姆的决定因素。
We study a $d$-dimensional random walk with exponentially distributed increments conditioned so that the components stay ordered (in the sense of Doob). We find explicitly a positive harmonic function $h$ for the killed process and then construct an ordered process using Doob's $h$-transform. Since these random walks are not nearest-neighbour, the harmonic function is not the Vandermonde determinant. The ordered process is related to the departure process of M/M/1 queues in tandem. We find asymptotics for the tail probabilities of the time until the components in exponential random walks become disordered and a local limit theorem. We find the distribution of the processes of smallest and largest particles as Fredholm determinants.
