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We derive some additional results on the Bienyamé-Galton-Watson branching process with θ−linear fractional branching mechanism, as studied in [16]. This includes: the explicit expression of the limit laws in both the sub-critical cases and the super-critical cases with finite mean, the long-run behavior of the population size in the critical case, limit… (More)

Deterministic population growth models with power-law rates can exhibit a large variety of growth behaviors, ranging from algebraic, exponential to hyperexponential (finite time explosion). In this setup, selfsimilarity considerations play a key role, together with two time substitutions. Two stochastic versions of such models are investigated, showing a… (More)

Motivated by issues arising in population dynamics, we consider the problem of iterating a given analytic function a number of times. We use the celebrated technique known as Carleman linearization that turns (for a certain class of functions) this problem into simply taking the power of a real number. We expand this method, showing in particular that it… (More)

We study the impact on shape parameters of an underlying Bienaymé-Galton-Watson branching process (height, width and first hitting time), of having a non-spatial branching mechanism with infinite variance. Aiming at providing a comparative study of the spread of an epidemics whose dynamics is given by the modulus of a branching Brownian motion (BBM) we then… (More)

This paper is an attempt to formalize analytically the question raised in " World Population Explained: Do Dead People Outnumber Living, Or Vice Versa? " Huffington Post, [7]. We start developing simple determin-istic Malthusian growth models of the problem (with birth and death rates either constant or time-dependent) before running into both linear birth… (More)

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