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We consider a stochastic differential equation of the form dr t = (a − br t )dt + σr β t dW t , where a, b and σ are positive constants, β ∈ ( 1 2 , 1). We study the estimation of an unknown drift parameter (a, b) by continuous observations of a sample path {r t , t ∈ [0, T ]}. We prove the strong consistency and asymptotic normality of the maximum likelihood estimator. We propose another strongly consistent estimator, which generalizes an estimator proposed in Dehtiar et al. ( 2021) for β = 1 2 . The identification of the diffusion parameters σ and β is discussed as well.

We consider a stochastic differential equation of the form dr t = (awhere a, b and σ are positive constants. The solution corresponds to the Cox-Ingersoll-Ross process. We study the estimation of an unknown drift parameter (a, b) by continuous observations of a sample path {r t , t ∈ [0, T ]}. First, we prove the strong consistency of the maximum likelihood estimator. Since this estimator is well-defined only in the case 2a > σ 2 , we propose another estimator that is defined and strongly consistent for all positive a, b, σ.The quality of the estimators is illustrated by simulation results.