{"ID":2855374,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.14023","arxiv_id":"2510.14023","title":"Filtering Problem for Random Processes with Stationary Increments","abstract":"This paper deals with the problem of optimal mean-square filtering of the linear functionals $Aξ=\\int_{0}^{\\infty}a(t)ξ(-t)dt$ and $A_Tξ=\\int_{0}^Ta(t)ξ(-t)dt$ which depend on the unknown values of random process $ξ(t)$ with stationary $n$th increments from observations of process $ξ(t)+η(t)$ at points $t\\leq0$, 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.","short_abstract":"This paper deals with the problem of optimal mean-square filtering of the linear functionals $Aξ=\\int_{0}^{\\infty}a(t)ξ(-t)dt$ and $A_Tξ=\\int_{0}^Ta(t)ξ(-t)dt$ which depend on the unknown values of random process $ξ(t)$ with stationary $n$th increments from observations of process $ξ(t)+η(t)$ at points $t\\leq0$, where...","url_abs":"https://arxiv.org/abs/2510.14023","url_pdf":"https://arxiv.org/pdf/2510.14023v1","authors":"[\"Maksym Luz\",\"Mykhailo Moklyachuk\"]","published":"2025-10-15T19:04:12Z","proceeding":"math.ST","tasks":"[\"math.ST\"]","methods":"[]","has_code":false}