Nonparametric Estimation in Continuous-state Branching Processes with Immigration

We study the nonparametric estimation of the intensity of the Poisson random measure in continuous-state branching processes with immigration based on the low frequency observations. This is given in terms of the minimization of norms on a nonempty, closed and convex subset in a special Hilbert space. We establish the measurability of the estimators and derive their consistency and asymptotic risk bounds under some conditions.