本文選題：具有相關(guān)噪聲的快慢隨機(jī)偏微分系統(tǒng) + 極大似然估計(jì)�。� 參考：《南京大學(xué)》2017年碩士論文

【摘要】：本文利用極大似然估計(jì)方法給出了具有相關(guān)噪聲的快慢隨機(jī)偏微分系統(tǒng)中的未知參數(shù)的估計(jì)量,并證明了該估計(jì)量的一致性。首先利用Radon-Nikodym定理直接得到具有相關(guān)噪聲的快慢隨機(jī)偏微分系統(tǒng)中參數(shù)的極大似然估計(jì)。然后對具有相關(guān)噪聲的快慢隨機(jī)偏微分系統(tǒng)利用有限維逼近,將有限維的具有相關(guān)噪聲的快慢隨機(jī)偏微分系統(tǒng)的數(shù)據(jù)直接帶入上述極大似然估計(jì)函數(shù)中,作為有限維具有相關(guān)噪聲的快慢隨機(jī)偏微分系統(tǒng)的參數(shù)估計(jì)。最后利用逼近得到該參數(shù)估計(jì)得一致性。從而得到具有相關(guān)噪聲的快慢隨機(jī)偏微分系統(tǒng)中未知參數(shù)的極大似然估計(jì)。
[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.
【學(xué)位授予單位】：南京大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O211.63
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本文編號：2079605