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Published in:
2015 | OriginalPaper | Chapter
4. Continuous State Branching Processes
Authors : Vincent Bansaye, Sylvie Méléard
Published in: Stochastic Models for Structured Populations
Publisher: Springer International Publishing
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Abstract
In this part, we consider a new class of stochastic differential equations for monotype populations, taking into account exceptional events where an individual has a large number of offspring. We generalize the Feller equation (3.12) obtained in Subsection 3.2 by adding jumps whose rates are proportional to the population size. The jumps are driven by a Poisson point measure, as already done in Subsection 2.4 This class of processes satisfies the branching property: the individuals of the underlying population evolve independently. Combining this property with the tools developed in the first part, we describe finely the processes, their long time behavior, and the scaling limits they come from.