On Minimality and Interpolation of Harmonizable Stable Processes

It is shown that a harmonizable symmetric $\alpha $-stable process, i.e. the Fourier coefficients of a process with independent symmetric $\alpha $-stable increments, with spectral density w is minimal, if and only if $w > 0$ a.e. and $w^{ - 1/(\alpha - 1)} \in L^1 $. Algorithms for the linear interpolator and interpolation error of such processes are given when several values of the process are missing. The algorithm, for the linear interpolator is convergent if w satisfies Muckenhoupt’s $(A_\alpha )$ condition.