We study the parameter estimation of two-type continuous-state branching processes with immigration based on low frequency observations at equidistant time points. The ergodicity of the processes is proved. The estimators are based on the minimization of a sum of squared deviation about...

A class of two-type continuous-state branching processes with immigration and competition is constructed as the solution of a jump-type stochastic integral equation system. We first show that the stochastic equation system has a pathwise unique non-negative strong solution and then prove the...

Markovian binary trees form a class of continuous-time branching processes where the lifetime and reproduction epochs of individuals are controlled by an underlying Markov process. An Expectation–Maximization (EM) algorithm is developed to estimate the parameters of the Markov process from the...

We study two models of population with migration. On an island lives an individual whose genealogy is given by a critical Galton–Watson tree. If its offspring ends up consuming all the resources, any newborn child has to migrate to find new resources. In this sense, the migrations are...

In the present paper, we characterize the behavior of supercritical branching processes in random environment with linear fractional offspring distributions, conditioned on having small, but positive values at some large generation. As it has been noticed in previous works, there is a phase...

We consider a continuous-time Markov chain with a finite or countable state space. For a site y and subset H of the state space, the hitting time of y under taboo H is defined to be infinite if the process trajectory hits H before y, and the first hitting time of y otherwise. We investigate the...

We consider a one dimensional ballistic random walk evolving in an i.i.d. parametric random environment. We provide a maximum likelihood estimation procedure of the parameters based on a single observation of the path till the time it reaches a distant site, and prove that the estimator is...