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

We consider the problem of the optimal linear estimation of the functional ANξ=∑k=0Na(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, 1<α≤2. The derived estimates are based on observations at points m∈Z∖{0,1,2,…,N}. Cases of observations without noise, with harmonizable symmetric α-stable noise and with noise with harmonizable symmetric α-stable increments are studied. Classical solutions as well as minimax robust ones are obtained.