On parameter estimation for critical affine processes

Abstract

First we provide a simple set of sufficient conditions for the weak convergence of scaled affine processes with state space $\mathbb{R}_{+}\times \mathbb{R}^{d}$. We specialize our result to one-dimensional continuous state branching processes with immigration. As an application, we study the asymptotic behavior of least squares estimators of some parameters of a two-dimensional critical affine diffusion process.