On interpolation problem for multidimensional harmonizable stable sequences with noise observations

We consider the problem of optimal linear estimation of the functional $$A_N\vec{\xi }=\sum _{j=0}^N(\vec{a}(j){)}^{\mathrm{\top }}\vec{\xi }(j)$$ that depends on the unknown values $\vec{\xi }(j),j=0,1,\dots ,N,$ of a vector-valued harmonizable symmetric $\alpha$-stable random sequence $\vec{\xi }(j)={\{{\xi }_k(j)\}}_{k=1}^T$, from observations of the sequence $\vec{\xi }(j)+\vec{\eta }(j)$ at points $j\in \mathbb{Z}\setminus \{0,1,\dots ,N\}$. We consider the problem for mutually independent vector-valued harmonizable symmetric $\alpha$-stable random sequences $\vec{\xi }(j)={\{{\xi }_k(j)\}}_{k=1}^T$ and $\vec{\eta }(j)={\{{\xi }_k(j)\}}_{k=1}^T$ which have absolutely continuous spectral measures and the spectral densities $f(\theta )$ and $g(\theta )$ satisfying the minimality condition.