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Abstract and Applied Analysis
Volume 2014, Article ID 473681, 6 pages
Research Article

Statistical Inference for Stochastic Differential Equations with Small Noises

1School of Mathematics and Statistics, Central South University, Changsha, Hunan 410075, China
2School of Science, Linyi University, Linyi, Shandong 276005, China

Received 13 November 2013; Accepted 11 February 2014; Published 13 March 2014

Academic Editor: Zhi-Bo Huang

Copyright © 2014 Liang Shen and Qingsong Xu. 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.


This paper proposes the least squares method to estimate the drift parameter for the stochastic differential equations driven by small noises, which is more general than pure jump -stable noises. The asymptotic property of this least squares estimator is studied under some regularity conditions. The asymptotic distribution of the estimator is shown to be the convolution of a stable distribution and a normal distribution, which is completely different from the classical cases.