TY - JOUR
T1 - A note on quasi-stationary distributions of birth-death processes and the SIS logistic epidemic
AU - Clancy, Damian
AU - Pollett, Philip
PY - 2003
Y1 - 2003
N2 - For Markov processes on the positive integers with the origin as an absorbing state, Ferrari, Kesten, Martínez and Picco studied the existence of quasi-stationary and limiting conditional distributions by characterizing quasi-stationary distributions as fixed points of a transformation Φ on the space of probability distributions on {1, 2,...}. In the case of a birth-death process, the components of Φ(ν) can be written down explicitly for any given distribution ν. Using this explicit representation, we will show that Φ preserves likelihood ratio ordering between distributions. A conjecture of Kryscio and Lefèvre concerning the quasi-stationary distribution of the SIS logistic epidemic follows as a corollary.
AB - For Markov processes on the positive integers with the origin as an absorbing state, Ferrari, Kesten, Martínez and Picco studied the existence of quasi-stationary and limiting conditional distributions by characterizing quasi-stationary distributions as fixed points of a transformation Φ on the space of probability distributions on {1, 2,...}. In the case of a birth-death process, the components of Φ(ν) can be written down explicitly for any given distribution ν. Using this explicit representation, we will show that Φ preserves likelihood ratio ordering between distributions. A conjecture of Kryscio and Lefèvre concerning the quasi-stationary distribution of the SIS logistic epidemic follows as a corollary.
U2 - 10.1017/S002190020001977X
DO - 10.1017/S002190020001977X
M3 - Article
SN - 0021-9002
VL - 40
SP - 821
EP - 825
JO - Journal of Applied Probability
JF - Journal of Applied Probability
ER -