共查询到6条相似文献,搜索用时 3 毫秒
1.
James Allen Fill 《Journal of Theoretical Probability》2009,22(3):587-600
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 ν
j
of the generator on {0,…,d}, with d made absorbing, are all real, their result states that the passage time is distributed as the sum of d independent exponential random variables with rates ν
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.
Research supported by NSF grant DMS–0406104, and by The Johns Hopkins University’s Acheson J. Duncan Fund for the Advancement
of Research in Statistics. 相似文献
2.
Jacek Gilewicz Elie Leopold Andreas Ruffing Galliano Valent 《Constructive Approximation》2006,24(1):71-89
The orthogonal polynomials with recurrence relation
(λ,n +μn-z)Fn(z) = μn+1Fn+1(z)+λn-1Fn-1(z) with two kinds of cubic transition rates λn and μn, corresponding to indeterminate Stieltjes moment problems, are analyzed. We derive generating functions for these two classes
of polynomials, which enable us to compute their Nevanlinna matrices. We discuss the asymptotics of the Nevanlinna matrices
in the complex plane. 相似文献
3.
In this paper we study a transient birth and death Markov process penalized by its sojourn time in 0. Under the new probability
measure the original process behaves as a recurrent birth and death Markov process. We also show, in a particular case, that
an initially recurrent birth and death process behaves as a transient birth and death process after penalization with the
event that it can reach zero in infinite time. We illustrate some of our results with the Bessel random walk example. 相似文献
4.
5.
生灭型半马氏骨架过程 总被引:1,自引:0,他引:1
本文首先引进了生灭型半马氏骨架过程的定义,求出了两骨架时跳跃点τn-1(ω)与τn(ω)之间的嵌入过程X(n)(t,ω)的初始分布及寿命分布.得到了生灭型半马氏骨架过程的一维分布.其次引进了生灭型半马氏骨架过程的数字特征并讨论了它们的概率意义及相互关系.讨论了生灭型半马氏骨架过程的向上和向下的积分型随机泛函.最后讨论了它的遍历性及平稳分布,求出了平均首达时间及平均返回时间.得到了常返和正常返的充分必要条件,求出了在正常返的条件下的平稳分布. 相似文献