| Article ID: | iaor19891051 |
| Country: | Netherlands |
| Volume: | 32 |
| Issue: | 1 |
| Start Page Number: | 161 |
| End Page Number: | 170 |
| Publication Date: | Jun 1989 |
| Journal: | Stochastic Processes and Their Applications |
| Authors: | Pakis Anthony G., Pollett P.K. |
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.