Asymptotic Behavior of the Maximum Likelihood Estimator for Ergodic and Nonergodic Square-Root Diffusions

This article deals with the problem of global parameter estimation in the Cox-Ingersoll-Ross (CIR) model (X-t)(t0). This model is frequently used in finance for example, to model the evolution of short-term interest rates or as a dynamic of the volatility in the Heston model. In continuity with a recent work by Ben Alaya and Kebaier [<xref rid="CIT0001" ref-type="bibr">1</xref>], we establish new asymptotic results on the maximum likelihood estimator (MLE) associated to the global estimation of the drift parameters of (X-t)(t0). To do so, we need to study the asymptotic behavior of the quadruplet . This allows us to obtain various and original limit theorems on our MLE, with different rates and different types of limit distributions. Our results are obtained for both cases: ergodic and nonergodic diffusion.