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Stochastic ordering for birth–death processes with killing
- Source :
- Journal of Applied Probability. 58:708-720
- Publication Year :
- 2021
- Publisher :
- Cambridge University Press (CUP), 2021.
-
Abstract
- We consider a birth–death process with killing where transitions from state i may go to either state $i-1$ or state $i+1$ or an absorbing state (killing). Stochastic ordering results on the killing time are derived. In particular, if the killing rate in state i is monotone in i, then the distribution of the killing time with initial state i is stochastically monotone in i. This result is a consequence of the following one for a non-negative tri-diagonal matrix M: if the row sums of M are monotone, so are the row sums of $M^n$ for all $n\ge 2$ .
Details
- ISSN :
- 14756072 and 00219002
- Volume :
- 58
- Database :
- OpenAIRE
- Journal :
- Journal of Applied Probability
- Accession number :
- edsair.doi...........73dff0382e71fb8f7e5489306748746f