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...

In this paper we consider the Cox correlated risk model perturbed by a diffusion (Wiener) process. We first derive an analog of the Bernstein-Kolmogorov inequality for the probabilities of large deviations of Cox random sums. Then an exponential upper-bound which deals with the estimate of ruin...