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Under natural assumptions a Feller type diffusion approximation is derived for critical multi-type branching processes with immigration when the offspring mean matrix is primitive (in other words, pos...
A study by University of Queensland and international researchers has found that most of Madagascar’s unique present-day fauna may originally have arrived across long distances by air or sea.
Abstract: We discover death-immigration non-equilibrium stochastic dynamics in the continuum also known as the Surgailis process. Explicit expression for the correlation functions is presented. Dynami...
Abstract: We investigate the inhomogeneous Galton--Watson processes with immigration, where $\rho_n$ the offspring means in the $n^\textrm{th}$ generation tends to 1. We show that if the second deriva...
Guided by the relationship between the breadth- rst walk of a rooted tree and its sequence of generation sizes, we extend the Lamperti representation of continuous-state branching processes to allow i...
We consider a general, neutral, dynamical model of biodiversity. Individuals have i.i.d. lifetime durations, which are not necessarily exponentially distributed, and each individual gives birth inde...
Epidemics that are either introduced into a population or fuelled by immigrating infective individuals are subject to dynamics that must include infectiveness external to the population itself. Immig...
The immigration dynamics of infectives is sometimes an imprescindable modelling feature to fully understand and explain the diffusion of important infections. The inclusion of the dynamics of individu...

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