Numerical simulation on maximum likelihood estimation of diffusion processes

In this paper, we consider parametric estimation problem of a continuous type stochastic mathematical model (stochastic differential equation) in a wide engineering field. On analyzing the probability characteristics of process, the density function is determined by using Ito differential law. The maximum-likelihood estimating (MLE) algorithm of unknown parameter is obtained. The approximation is calculated by using numerical solution techniques for diffusion process. Finally, we consider three methods for solving the Cox-Ingersoll-Ross process as a numerical example. © Metallurgical and Mining Industry, 2015.