On extrapolation of transformations of random processes disturbed by the white noise - Moklyachuk , M. P. (Ukrains’kyi Matematychnyi Zhurnal, 2025)
We consider the problem of linear mean square optimal estimation of transformation Aξ = _0^∞a(t)ξ (t) dt of a stationary random process ξ (t) in observations of process ξ (t)+η(t) for t≤ 0, where η (t) is white noise uncorrelated with ξ (t). We find least favorable spectral densities f_0(λ) D and minimax (robust) spectral characteristics of an optimal estimator of transformation Aξ for various classes D of densities.