A characterization of subclasses of semi-selfdecomposable distributions by stochastic integral representations

Characterizations of the classes of selfdecomposable (semi-selfdecomposable, resp.) by a stochastic integral with respect to Lévy process (semi-Lévy process, resp.) are known. A similar characterization for the Urbanik-Sato nested subclasses of the class of selfdecomposable distributions is also known. In this paper, a characterization of the nested subclasses of the class of semi-selfdecomposable distributions is given in terms of stochastic integral with respect to semi-Lévy process.