Abstract
The theory of Crump-Mode-Jagers branching processes gives us the expected future population as a solution of a renewal equation. In order to find the expected future population age structure a large amount of renewal equations must be solved. This paper presents a numerical approach for projecting the population age structure and solving these renewal equations based on the theory of General Branching Processes. It is shown that the Leslie matrix projection, widely used in demographics, is actually a special case of this method. Applying the continuous time theory of branching processes produces estimation error for the Leslie matrix projections that comes from discretization of time. The presented numerical method can also be used for solving renewal equations satisfying certain conditions of smoothness. It involves only simple matrix multiplications which results in a very fast calculation speed.
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