TY - JOUR
AU - Maksym Luz
AU - Mikhail Moklyachuk
PY - 2023/07/08
Y2 - 2024/10/11
TI - Estimation problem for continuous time stochastic processes with periodically correlated increments
JF - Statistics, Optimization & Information Computing
JA - Stat., optim. inf. comput.
VL - 11
IS - 4
SE - Research Articles
DO - 10.19139/soic-2310-5070-1792
UR - http://iapress.org/index.php/soic/article/view/1792
AB - 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.
ER -