### Abstract

Original language | English |
---|---|

Pages (from-to) | 120-145 |

Journal | Advances in Applied Probability |

Volume | 27 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1995 |

### Fingerprint

### Cite this

}

*Advances in Applied Probability*, vol. 27, no. 1, pp. 120-145. https://doi.org/10.2307/1428100

**QUASI-Stationary laws for Markov Processes: Examples of an always proximate absorbing state.** / Pakes, Anthony.

Research output: Contribution to journal › Article

TY - JOUR

T1 - QUASI-Stationary laws for Markov Processes: Examples of an always proximate absorbing state

AU - Pakes, Anthony

PY - 1995

Y1 - 1995

N2 - Under consideration is a continuous-time Markov process with non-negative integer state space and a single absorbing state 0. Let T be the hitting time of zero and suppose P-i(T x)P(i)(T > t) = 1 for all t > 0. Most known cases satisfy (*). The Markov process has a quasi-stationary distribution iff E(i)(e(epsilon T)) 0.The published proof of this fact makes crucial use of (*). By means of examples it is shown that (*) can be violated in quite drastic ways without destroying the existence of a quasi-stationary distribution.

AB - Under consideration is a continuous-time Markov process with non-negative integer state space and a single absorbing state 0. Let T be the hitting time of zero and suppose P-i(T x)P(i)(T > t) = 1 for all t > 0. Most known cases satisfy (*). The Markov process has a quasi-stationary distribution iff E(i)(e(epsilon T)) 0.The published proof of this fact makes crucial use of (*). By means of examples it is shown that (*) can be violated in quite drastic ways without destroying the existence of a quasi-stationary distribution.

U2 - 10.2307/1428100

DO - 10.2307/1428100

M3 - Article

VL - 27

SP - 120

EP - 145

JO - Advances in Applied Probability (SGSA)

JF - Advances in Applied Probability (SGSA)

SN - 0001-8678

IS - 1

ER -