无跳链和更一般链的首中时和最快强平稳时
On hitting times and fastest strong stationary times for skip-free and more general chains
摘要：
以非负整数的集合作为状态空间的（向上）无跳马尔可夫链是这样的链，其中向上的跳跃可能只有单位大小，向下的跳跃没有限制。在1987年的一篇论文中，布朗和邵确定了一个不可约的连续时间无跳跃链和任何d，从状态0到状态d的通过时间分布。当生成元的非零特征值nu_j均为实数时，他们的结果表明，通过时间服从d个独立指数随机变量之和的分布，其速率为nu_j.本文给出了他们定理的另一个证明.在生死链的情况下，我们的证明导致一个明确的表示的通过时间作为一个独立的指数随机变量的总和。Diaconis和Miclo最近获得了第一个这样的表示，但我们的构造要简单得多。我们得到了类似的（和新的）结果的最快的强平稳时间T的遍历连续时间跳跃无链与随机单调时间反转开始于状态0，我们也得到了离散时间模拟我们所有的结果。在本文的最后一节中，我们提出了我们的结果更一般的链的扩展。
英文摘要：
An (upward) skip-free Markov chain with the set of nonnegative integers as state space is a chain for which upward jumps may be only of unit size; there is no restriction on downward jumps. In a 1987 paper, Brown and Shao determined, for an irreducible continuous-time skip-free chain and any d, the passage time distribution from state 0 to state d. When the nonzero eigenvalues nu_j of the generator are all real, their result states that the passage time is distributed as the sum of d independent exponential random variables with rates nu_j. We give another proof of their theorem. In the case of birth-and-death chains, our proof leads to an explicit representation of the passage time as a sum of independent exponential random variables. Diaconis and Miclo recently obtained the first such representation, but our construction is much simpler. We obtain similar (and new) results for a fastest strong stationary time T of an ergodic continuous-time skip-free chain with stochastically monotone time-reversal started in state 0, and we also obtain discrete-time analogs of all our results. In the paper's final section we present extensions of our results to more general chains.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
