Filtering Problem for Random Processes with Stationary Increments

2025/10/15 by Luz, Maksym, Moklyachuk, Mykhailo · 1 citation
#60G25 #FOS: Mathematics #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.2510.14023

Abstract

This paper deals with the problem of optimal mean-square filtering of the linear functionals Aξ=∫₀^∞a(t)ξ(-t)dt and A_Tξ=∫₀^Ta(t)ξ(-t)dt which depend on the unknown values of random process ξ(t) with stationary nth increments from observations of process ξ(t)+η(t) at points t≤0, where η(t) is a stationary process uncorrelated with ξ(t). We propose the values of mean-square errors and spectral characteristics of optimal linear estimates of the functionals when spectral densities of the processes are known. In the case where we can operate only with a set of admissible spectral densities relations that determine the least favorable spectral densities and the minimax spectral characteristics are proposed.

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