Stable and semistable hemigroups: Domains of attraction and self-decomposability (Q1411346)

The author obtains descriptions of stable and semi-stable convolution hemigroups as limits in certain functional limit theorems for operator-normed sequences of independent random vectors (not necessarily identically distributed). This functional limit law is closely related to a limit law of infinitesimal triangular arrays of random vectors, which establishes a relation between (semi-)stable hemigroups and operator-(semi-) self-decomposable measures. Generalized domains of attraction are defined and investigated for the above classes of hemigroups.