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.

翻译：考虑从具有周期相关增量的连续时间随机过程的未观测值构造的线性泛函的最优估计问题，该估计基于该过程的过去观测值。为求解该问题，我们构造了与过程相对应的随机函数序列，该序列形成无限维向量平稳增量序列。在平稳增量序列的谱密度已知的情况下，我们获得了计算泛函最优估计均方误差值及谱特征的公式。当给定可容许谱密度集合时，推导出确定最不利谱密度以及泛函最优线性估计极小极大（鲁棒）谱特征的公式。