The problem of optimal estimation of linear functionals $A {\xi}=\int_{0}^{\infty} a(t)\xi(t)dt$ and $A_T{\xi}=\int_{0}^{T} a(t)\xi(t)dt$ depending on the unknown values of random process $\xi(t)$, $t\in R$, with stationary $n$th increments from observations of ttis process for $t<0$ is considered. Formulas for calculating mean square error and spectral characteristic of optimal linear estimation of the functionals are proposed in the case when spectral density is exactly known. Formulas that determine the least favorable spectral densities are proposed for given sets of admissible spectral densities.

翻译：本文考虑基于 $t<0$ 时对随机过程 $\xi(t)$ ($t\in R$) 的观测，对依赖于该过程未知值的线性泛函 $A {\xi}=\int_{0}^{\infty} a(t)\xi(t)dt$ 和 $A_T{\xi}=\int_{0}^{T} a(t)\xi(t)dt$ 进行最优估计的问题，其中该过程具有 $n$ 阶平稳增量。在谱密度精确已知的情况下，提出了用于计算最优线性估计的均方误差和谱特征的公式。对于给定的容许谱密度集合，提出了确定最不利谱密度的公式。