  Stable non-Gaussian self-similar mixed moving averages can be decomposed into
several components. Two of these are the periodic and cyclic fractional stable
motions which are the subject of this study. We focus on the structure of their
integral representations and show that the periodic fractional stable motions
have, in fact, a canonical representation. We study several examples and
discuss questions of uniqueness, namely how to determine whether two given
integral representations of periodic or cyclic fractional stable motions give
rise to the same process.
