Uniform Approximate Estimation for Nonlinear Nonhomogenous Stochastic System with Unknown Parameter

The error bound in probability between the approximate maximum likelihood estimator (AMLE) and the continuous maximum likelihood estimator (MLE) is investigated for nonlinear nonhomogenous stochastic system with unknown parameter. The rates of convergence of the approximations for Ito and ordinary integral are introduced under some regular assumptions. Based on these results, the in probability rate of convergence of the approximate log-likelihood function to the true continuous log-likelihood function is studied for the nonlinear nonhomogenous stochastic system involving unknown parameter. Finally, the main result which gives the error bound in probability between the ALME and the continuous MLE is established.