Extinction Probability in a Birth-death Process with Killing

@inproceedings{Doorn2004ExtinctionPI,
  title={Extinction Probability in a Birth-death Process with Killing},
  author={Erik A. van Doorn and Alexander I. Zeifman and Sofia Orlova},
  year={2004}
}
We study birth–death processes on the nonnegative integers, where {1, 2, . . . } is an irreducible class and 0 an absorbing state, with the additional feature that a transition to state 0 may occur from any state. We give a condition for absorption (extinction) to be certain and obtain the eventual absorption probabilities when absorption is not certain. We also study the rate of convergence, as t → ∞, of the probability of absorption at time t , and relate it to the common rate of convergence… CONTINUE READING

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