On Minimax Robust Estimation Problem for Stochastic Sequences with Harmonizable Stable Increments

We consider the problem of optimal linear estimation of the functional A_Nξ = ∑^N_k=0 a(k)ξ(k) which depends on the unknown values ξ(k), k = 0,1,...,N, of a stochastic sequence with harmonizable symmetric α-stable nth increments. The derived estimates are based on observations at points m ∈ Z \ {0,1,2,...,N}. The cases of observations without noise, with harmonizable symmetric α-stable noise and with noise having harmonizable symmetric α-stable increments are studied. The classical solutions as well as the minimax robust ones are obtained.