The supercritical birth, death and catastrophe process: limit theorems on the set of extinction

Anthony G. Pakes and P. K. Pollett

Stochastic Processes and their Applications, 1989, vol. 32, issue 1, 161-170

Abstract: 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

Keywords: Markovian; population; process; Markov; branching; process; quasi-stationary; distribution (search for similar items in EconPapers)
Date: 1989
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