具有周期相关增量的随机过程的滤波
Filtering of stochastic processes having periodically correlated increments
AI总结：
本文针对具有周期相关增量的连续时间随机过程，通过转化为无限维平稳序列，求解其线性变换的均方最优估计，并给出误差、谱特征及极小极大稳健估计公式。
摘要：
本文研究了具有周期相关增量的连续时间随机过程的未观测值的线性变换的均方最优估计问题。估计基于对该过程及其连续时间随机噪声过程的观测，该噪声过程同样具有周期相关增量。为解决该问题，我们将这些过程转化为无限维向量值平稳序列。我们获得了计算这些变换的最优估计的均方误差和谱特征的公式。此外，还推导了确定最不利谱密度以及变换的最优估计的极小极大稳健谱特征的公式。
英文摘要：
We deal with the problem of the mean square optimal estimation of linear transformations of the unobserved values of a continuous time stochastic process with periodically correlated increments. Estimates are based on observations of the process with a continuous time stochastic noise process which is periodically correlated increments as well. To solve the problem, we transform the processes to infinite dimensional vector valued stationary sequences. We obtain formulas for calculating the mean square errors and the spectral characteristics of the optimal estimates of the transformations. Formulas determining the least favorable spectral densities and the minimax-robust spectral characteristics of the optimal estimates of transformations are derived.
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