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Gaussian estimation for discretely observed Cox-Ingersoll-Ross model. (English) Zbl 1342.93110

Summary: This paper is concerned with the parameter estimation problem for Cox-Ingersoll-Ross model based on discrete observation. First, a new discretized process is built based on the Euler-Maruyama scheme. Then, the parameter estimators are obtained by employing the maximum likelihood method and explicit expressions of the error of estimation are given. Subsequently, the consistency property of all parameter estimators are proved by applying the law of large numbers for martingales, Hölder’s inequality, B-D-G inequality and Cauchy-Schwarz inequality. Finally, a numerical simulation example for estimators and the absolute error between estimators and true values is presented to demonstrate the effectiveness of the estimation approach used in this paper.

MSC:

93E10 Estimation and detection in stochastic control theory
93C73 Perturbations in control/observation systems
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
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