2023/04/24 by Maksym Luz, Luz, Maksym, Mikhail Moklyachuk +1
Environmental Science · #60G25 #60G35 #62P20 #93E10 #93E11 #Analysis of environmental and stochastic processes #FOS: Mathematics #Primary: 60G10 #Scientific Research and Studies #Secondary: 62M20 #Statistics Theory (math.ST) #Water Resources and Management
paper · pdf · doi:10.48550/arxiv.2304.12220
openalex publication_date 2023/04/24 · openalex created_date 2023/04/27 · openalex updated_date 2026/07/28
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.