Continuity for multi-type branching processes with varying environments

Owen Dafydd Jones

Abstract: Conditions are derived for the components of the normed limit of a multi-type branching process with varying environments, to be continuous on (0, \infty). The main tool is an inequality for the concentration function of sums of independent random variables, due originally to Petrov. Using this, we show that if there is a discontinuity present, then a particular linear combination of the population types must converge to a non-random constant (Equation (1)). Ensuring this can not happen provides the desired continuity conditions.

Acknowledgement: This worked was funded by the Australian Research Council.

The author:

• Owen Jones, Discipline of Mathematics, The University of Queensland. Owen.Jones@maths.anu.edu.au

Back to Research Communications

Back to PKP's home page

Last modified: 6th July 1998