Filtering of stochastic processes having periodically correlated increments

2024/02/02 by Maksym Luz, Luz, Maksym, Mikhail Moklyachuk +1
Computer Science · #60G10 #60G25 #60G35 #62M20 #62P20 #93E10 #93E11 #FOS: Mathematics #Statistical and Computational Modeling #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.2402.06396

openalex publication_date 2024/02/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We deal with the problem of the mean square optimal estimation of linear transformations of the unobserved values of a continuous time stochastic process with periodically correlated increments. Estimates are based on observations of the process with a continuous time stochastic noise process which is periodically correlated increments as well. To solve the problem, we transform the processes to infinite dimensional vector valued stationary sequences. We obtain formulas for calculating the mean square errors and the spectral characteristics of the optimal estimates of the transformations. Formulas determining the least favorable spectral densities and the minimax-robust spectral characteristics of the optimal estimates of transformations are derived.

Related

• Estimation problem for continuous time stochastic processes with periodically correlated increments
• Filtering of periodically correlated processes
• Prediction problem for continuous time stochastic processes with periodically correlated increments observed with noise
• Minimax Estimation Problem for Periodically Correlated Stochastic Processes
• Minimax interpolation of continuous time stochastic processes with periodically correlated increments observed with noise