From the introduction: Diffusion processes play important roles in the study of mathematical finance and other applications. In those applications we need to identify the models with unknown parameters [see B. L. S. Prakasa Rao, Statistical inference for diffusion type processes. (1999; Zbl 0952.62077)]. We consider the maximum likelihood estimator of the following diffusion process: \[ dY_t=\sigma(Y_t,t,\theta) dW_t+b(Y_t,t,\theta)dt,\quad Y_0=y_0, \] where \(\theta\) is an unknown parameter and \(W_t\) is a standard Wiener process. Without loss of generality we assume that \(\theta\in\Theta\) where \(\Theta\) is a bounded interval with length 1 and that there is a constant \(0<c<\infty\) such that \(c<\sigma(.,.,.)<1/c\). Moreover we assume that both \(\sigma\) and \(b\) are Lipschitz in all of their arguments. We give a precise estimate for the error of the estimator.