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.
Highlights
To the best knowledge of the authors the parameter estimation problem for multi-dimensional affine processes has not been tackled so far
Since affine processes are being used in financial mathematics very frequently, the question of parameter estimation for them is of high importance
Our aim is to start the discussion with a simple non-trivial example: the two-dimensional affine diffusion process given by (1.1)
Summary
Let N, Z+, R, R+, R−, R++, and C denote the sets of positive integers, non-negative integers, real numbers, non-negative real numbers, non-positive real numbers, positive real numbers and complex numbers, respectively. We note that the existence of a pathwise unique strong solution (Yt, Xt)t∈R+ of the SDE (3.1) with P(Yt 0 for all t ∈ R+) = 1 follows by a general result of Dawson and Li [10, Theorem 6.2]. 2.4] studied asymptotic behaviour of weighted conditional least squares estimator of the drift parameters for discretely observed continuous time critical branching processes with immigration given by t. Huang et al [20] investigated the asymptotic behaviour of weighted conditional least squares estimator of the drift parameters for critical continuous time branching processes with immigration, and for subcritical and supercritical ones. The other critical and non-critical cases are under investigation but different techniques are needed
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