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Additional quasi-stationary distributions for semi-Markov processes
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- Journal:
- Journal of Applied Probability / Volume 9 / Issue 3 / June 1972
- Published online by Cambridge University Press:
- 14 July 2016, pp. 671-676
- Print publication:
- June 1972
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- Article
- Export citation
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Consider a semi-Markov process X(t) defined on a subset of the non-negative integers with zero as an absorbing state and the non-zero states forming an irreducible class with exit to zero being possible. Conditions are given for the existence of the limits:
where Xj(t) is the amount of time prior to time t spent in state j.The limits (which are independent of the initial state) are evaluated when the sufficient conditions are satisfied.
