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In the application of kriging model in the field of simulation, the parameters of the model are likely to be estimated from the simulated data. This introduces parameter estimation uncertainties into the overall prediction error, and this uncertainty can be further aggravated by random noise in stochastic simulations. In this paper, we study the effects of stochastic noise on parameter estimation and the overall prediction error. A two-point tractable problem and three numerical experiments are provided to show that the random noise in stochastic simulations can increase the parameter estimation uncertainties and the overall prediction error. Among the three kriging model forms studied in this paper, the modified nugget effect model captures well the various components of uncertainty and has the best performance in terms of the overall prediction error.