Asymptotic Behavior of The Maximum Likelihood Estimator For Ergodic and Nonergodic Sqaure-Root Diffusions

This paper deals with the problem of global parameter estimation in the Cox-IngersollRoss (CIR) model (Xt)t≥0. 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 [1], we establish new asymptotic results on the maximum likelihood estimator (MLE) associated to the global estimation of the drift parameters of (Xt)t≥0. To do so, we need to study first the asymptotic behavior of the quadruplet (log Xt, Xt, ∫ t 0 Xsds, ∫ t 0 ds Xs ). 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. AMS 2000 Mathematics Subject Classification. 44A10, 60F05, 62F12.