# Quasi-stationary laws for Markov processes: Examples of an always proximate absorbing state

Research output: Contribution to journalLetter

### Abstract

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) = 1 and (*) lim(i-->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)) <infinity for some epsilon > 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.
Original language English 30 Advances in Applied Probability 27 March (1) https://doi.org/10.2307/1428100 Published - 1995

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Quasi-stationary Distribution
Absorbing
Markov Process
Markov processes
Continuous-time Markov Process
Hitting Time
State Space
Non-negative
Integer
Zero

### Cite this

@article{2332fdcfbe154482beb66df1a32649e1,
title = "Quasi-stationary laws for Markov processes: Examples of an always proximate absorbing state",
abstract = "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.",
author = "Anthony Pakes",
year = "1995",
doi = "10.2307/1428100",
language = "English",
volume = "27",
pages = "30",
journal = "Advances in Applied Probability (SGSA)",
issn = "0001-8678",
publisher = "University of Sheffield",
number = "March (1)",

}

In: Advances in Applied Probability, Vol. 27, No. March (1), 1995, p. 30.

Research output: Contribution to journalLetter

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 - Letter

VL - 27

SP - 30

JO - Advances in Applied Probability (SGSA)

JF - Advances in Applied Probability (SGSA)

SN - 0001-8678

IS - March (1)

ER -