Abstract
A branching process is a \(\mathbb{Z}_{+}\)-valued process \(\{X_{t},\ t \in \mathbb{Z}_{+}\mbox{ or }t \in \mathbb{R}_{+}\}\) which is such that for each t, {X t+s , s > 0} is the sum of X t independent copies of {X s , s > 0}, where the latter starts from X 0 = 1. This type of process models the evolution of a population where the progenies of various individuals are i.i.d., i.e. there is no interaction between various contemporaneous individuals, whose fertility and lifetime have the same law. Models with interaction between the individuals will be studied below, starting with chapter 6
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References
E. Pardoux, Markov Processes and Applications. Algorithms, Networks, Genome and Finance. Wiley Series in Probability and Statistics (Wiley/Dunod, Chichester/Paris, 2008). Translated from the French original edition Processus de Markov et applications (Dunod, Paris, 2007)
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Pardoux, É. (2016). Branching Processes. In: Probabilistic Models of Population Evolution. Mathematical Biosciences Institute Lecture Series(), vol 1.6. Springer, Cham. https://doi.org/10.1007/978-3-319-30328-4_2
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DOI: https://doi.org/10.1007/978-3-319-30328-4_2
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