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Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 421754, 20 pages
http://dx.doi.org/10.1155/2012/421754
Research Article

Uniform Approximate Estimation for Nonlinear Nonhomogenous Stochastic System with Unknown Parameter

School of Information Science and Technology, Donghua University, Shanghai 200051, China

Received 21 June 2012; Accepted 3 August 2012

Academic Editor: Jun Hu

Copyright © 2012 Xiu Kan and Huisheng Shu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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 Itô 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.