The supercritical birth, death and catastrophe process: limit theorems on the set of extinction
The stationary conditional quasi-stationary distribution of the linear birth, death and catastrophe process is shown to exist iff the decrement distribution has a finite second order moment, Conditional limit theorems for the population size are found when this moment is infinite and a regular variation condition is satisfied. The relevance of the results in this paper to the general theory of quasi-stationary distributions is discussed
Year of publication: |
1989
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Authors: | Pakes, Anthony G. ; Pollett, P. K. |
Published in: |
Stochastic Processes and their Applications. - Elsevier, ISSN 0304-4149. - Vol. 32.1989, 1, p. 161-170
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Publisher: |
Elsevier |
Keywords: | Markovian population process Markov branching process quasi-stationary distribution |
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