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Stochastic ordering for birth–death processes with killing
Published online by Cambridge University Press: 16 September 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
$n\ge 2$
.
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- Original Article
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- Copyright
- © The Author(s), 2021. Published by Cambridge University Press on behalf of Applied Probability Trust
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