We introduce the <I>Hawkes process with renewal immigration</I> and make its statistical estimation possible with two <I>Expectation Maximization</I> (EM) algorithms. The standard <I>Hawkes process</I> introduces <I>immigrant points</I> via a Poisson process, and each immigrant has a subsequent cluster of associated...</i></i></i></i>

We provide sufficient conditions for polynomial rate of convergence in the weak law of large numbers for supercritical general indecomposable multi-type branching processes. The main result is derived by investigating the embedded single-type process composed of all individuals having the same...

We study the pruning process developed by Abraham and Delmas (2012) on the discrete Galton–Watson sub-trees of the Lévy tree which are obtained by considering the minimal sub-tree connecting the root and leaves chosen uniformly at rate λ, see Duquesne and Le Gall (2002). The tree-valued...

Poisson processes are used in various application fields applications (public health biology, reliability and so on). In their homogeneous version, the intensity process is a deterministic constant. In their inhomogeneous version, it depends on time. To allow for an endogenous evolution of the...