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We consider a stochastic differential equation of the form $dr_t = (a - br_t) dt + \sigma\sqrt{r_t}dW_t$, where $a$, $b$ and $\sigma$ are positiveconstants. The solution corresponds to the Cox-Ingersoll-Ross process. We studythe estimation of an unknown drift parameter $(a,b)$ by continuous observationsof a sample path $\{r_t,t\in[0,T]\}$. First, we prove the strong consistency ofthe maximum likelihood estimator. Since this estimator is well-defined only inthe case $2a>\sigma^2$, we propose another estimator that is defined andstrongly consistent for all positive $a$, $b$, $\sigma$. The quality of theestimators is illustrated by simulation results.

Two methods of estimation of the drift parameters of the Cox-Ingersoll-Ross process: continuous observations