张彩伢. 奇异随机偏微分方程中参数MLE的渐近性质[J]. 应用概率统计, 2015, 31(2): 183-192.
引用本文: 张彩伢. 奇异随机偏微分方程中参数MLE的渐近性质[J]. 应用概率统计, 2015, 31(2): 183-192.
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Zhang Caiya. Asymptotic Properties about MLE of the Parameter in Some Singular Stochastic Partial Differential Equation[J]. Chinese Journal of Applied Probability and Statistics, 2015, 31(2): 183-192.
Citation: Zhang Caiya. Asymptotic Properties about MLE of the Parameter in Some Singular Stochastic Partial Differential Equation[J]. Chinese Journal of Applied Probability and Statistics, 2015, 31(2): 183-192.
shu

奇异随机偏微分方程中参数MLE的渐近性质

Asymptotic Properties about MLE of the Parameter in Some Singular Stochastic Partial Differential Equation

    摘要
  • 摘要: 对一类带有未知参数和小干扰项的奇异随机偏微分方程, 基于连续样本轨道, 给出了参数的极大似然估计, 证明了当干扰项趋于0时, 参数估计量的强相合性和渐近正态性.

     

    Abstract: In this paper, the singular stochastic partial differential equation with an unknown parameter and a small noise is studied. The maximum likelihood estimator of the parameter based on the continuous observation of the Fourier coefficients is proposed. The strong convergence and asymptotic normality of the estimator are established as the noise tends to zero.

     

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