We provide a simple set of sufficient conditions for the weak convergence of two-type Galton-Watson branching processes with immigration to two-dimensional, continuous-time, continuous-state branching processes with immigration, which generalizes the limit result of Li [Li, Z.H., 2006a. A limit...

We introduce a class of interest rate models, called the α-CIR model, which gives a natural extension of the standard CIR model by adopting the α-stable L ́evy process and preserving the branching property. This model allows to describe in a unified and parsimonious way several recent...

The asymptotic estimation of drift parameter is studied for generalized Ornstein-Uhlenbeck processes with small Lévy noises. We extend the work of Long (2009) and show that the main results of Long (2009) hold under the weaker conditions.

We study the problem of parameter estimation for the continuous state branching processes with immigration, observed at discrete time points. The weighted conditional least square estimators (WCLSEs) are used for the drift parameters. Under the proper moment conditions, asymptotic distributions...

The central limit theorems, the deviation inequality (and large deviation), and the moderate deviations for least squares estimators of parameters in the CIR type model driven byα-stable noises are established when the dispersion parameter ε→0 and the discrete observation frequency k→∞...