Estimation problem for continuous time stochastic processes with periodically correlated increments

Keywords: Periodically Correlated Increments, Minimax-Robust Estimate, Mean Square Error

Abstract

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.

Author Biography

Mikhail Moklyachuk, Kyiv National Taras Shevchenko University
Department of Probability Theory, Statistics and Actuarial Mathematics, Professor

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Published
2023-07-08
How to Cite
Luz, M., & Moklyachuk, M. (2023). Estimation problem for continuous time stochastic processes with periodically correlated increments. Statistics, Optimization & Information Computing, 11(4), 811-828. https://doi.org/10.19139/soic-2310-5070-1792
Section
Research Articles