Author(s)

Zhiwei Zheng¹, Huisheng Shu^1*, Xiu Kan², Yingyi Fang¹, Xin Zhang¹

¹School of Science, Donghua University, Shanghai, China.
²School of Electronic and Electrical Engineering, Shanghai University of Engineering Science, Shanghai, China.

In this paper, the parameter estimation problem is investigated for the continuous time stochastic logistic diffusion system. A new continuous process is built based on the likelihood ratio scheme, the Radon-Nikodym derivative and the explicit expressions of the error of estimation are given under this new continuous process. By using the random time transformations, law of large numbers for martingales, law of iterated logarithm and stationary distribution of solution, the consistency property are proved for the estimation error. Finally, a numerical simulation is presented to demonstrate the effectiveness of the proposed method in this paper.

Parameter Estimation, Stationary Distribution, Likelihood Ratio, Random Time Transformations

Zheng, Z. , Shu, H. , Kan, X. , Fang, Y. and Zhang, X. (2017) Parameter Estimation for the Continuous Time Stochastic Logistic Diffusion Model. Open Journal of Statistics, 7, 1039-1052. doi: 10.4236/ojs.2017.76072.