具有周期相关增量的连续时间随机过程的估计问题

M. Luz, M. Moklyachuk
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引用次数: 1

摘要

我们处理的问题是线性泛函的最优估计由一个连续时间随机过程的未观测值构造的周期性相关增量基于该过程的过去的观测。为了解决这个问题,我们构造了一个与随机函数过程序列相对应的过程序列,它构成了一个无限维向量平稳增量序列。在已知平稳增量序列的谱密度的情况下,我们得到了计算均方误差值和函数最优估计的谱特征的公式。在给定可容许谱密度集合的情况下,导出了确定泛函最优线性估计的最不利谱密度和最小(鲁棒)谱特性的公式。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Estimation problem for continuous time stochastic processes with periodically correlated increments
We deal with the problem of optimal estimation of the linear functionals constructed from unobserved values of a continuous time stochastic process with periodically correlated increments based on past observations of this process. To solve the problem, we construct a corresponding to the process sequence of stochastic functions which forms an infinite dimensional vector stationary increment sequence. In the case of known spectral density of the stationary increment sequence, we obtain formulas for calculating values of the mean square errors and the spectral characteristics of the optimal estimates of the functionals. Formulas determining the least favorable spectral densities and the minimax (robust) spectral characteristics of the optimal linear estimates of functionals are derived in the case where the sets of admissible spectral densities are given.
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