快慢随机偏微分系统的极大似然估计

发布时间：2018-06-28 22:26

  本文选题：具有相关噪声的快慢随机偏微分系统 + 极大似然估计　； 参考：《南京大学》2017年硕士论文

【摘要】：本文利用极大似然估计方法给出了具有相关噪声的快慢随机偏微分系统中的未知参数的估计量,并证明了该估计量的一致性。首先利用Radon-Nikodym定理直接得到具有相关噪声的快慢随机偏微分系统中参数的极大似然估计。然后对具有相关噪声的快慢随机偏微分系统利用有限维逼近,将有限维的具有相关噪声的快慢随机偏微分系统的数据直接带入上述极大似然估计函数中,作为有限维具有相关噪声的快慢随机偏微分系统的参数估计。最后利用逼近得到该参数估计得一致性。从而得到具有相关噪声的快慢随机偏微分系统中未知参数的极大似然估计。
[Abstract]:In this paper, the estimator of unknown parameters in a fast and slow stochastic partial differential system with correlated noise is given by using the maximum likelihood estimation method, and the consistency of the estimator is proved. Firstly, the Radon-Nikodym theorem is used to obtain the maximum likelihood estimation of the parameters of fast and slow stochastic partial differential systems with correlated noise. Then the finite-dimensional approximation of the fast and slow stochastic partial differential systems with correlated noise is used to bring the data of the fast and slow stochastic partial differential systems with correlation noise directly into the above maximum likelihood estimation function. As the parameter estimation of fast and slow stochastic partial differential systems with correlation noise in finite dimension. Finally, the consistency of the parameter estimation is obtained by approximation. The maximum likelihood estimation of unknown parameters in fast and slow stochastic partial differential systems with correlated noise is obtained.
【学位授予单位】：南京大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O211.63
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本文编号：2079605