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Parameter Estimation for the Continuous Time Stochastic Logistic Diffusion Model
School of Science, Donghua University, Shanghai, China
School of Science, Donghua University, Shanghai, China
School of Electronic and Electrical Engineering, Shanghai University of Engineering Science, Shanghai, China
School of Science, Donghua University, Shanghai, China
School of Science, Donghua University, Shanghai, China
- 1 School of Science, Donghua University, Shanghai, China
- 2 School of Science, Donghua University, Shanghai, China
- 3 School of Electronic and Electrical Engineering, Shanghai University of Engineering Science, Shanghai, China
- 4 School of Science, Donghua University, Shanghai, China
- 5 School of Science, Donghua University, Shanghai, China
Open Journal of Statistics·Volume 07 (2017)·Pages 1039–1052·Published 15 November 2017·DOI10.4236/ojs.2017.76072
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Abstract
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.
KeywordsParameter EstimationStationary DistributionLikelihood RatioRandom Time Transformations
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