On hitting times and fastest strong stationary times for skip-free and more general chains
| dc.creator | Fill, James Allen | |
| dc.date | 2007-08-31 | |
| dc.date | 2009-05-06 | |
| dc.date.accessioned | 2026-07-07T13:11:37Z | |
| dc.date.available | 2026-07-07T13:11:37Z | |
| dc.description | 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. | |
| dc.description | To appear in Journal of Theoretical Probability. Main change: addition of final section | |
| dc.identifier | https://arxiv.org/abs/0708.4258 | |
| dc.identifier | http://arxiv.org/abs/0708.4258 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/229339 | |
| dc.subject | Probability | |
| dc.subject | 60J25 (Primary) 60J35, 60J10, 60G40 (Secondary) | |
| dc.title | On hitting times and fastest strong stationary times for skip-free and more general chains | |
| dc.type | text |