Minimal conditions in p-stable limit theorems -- II

A p-stable limit theorem holds for partial sums Sn of a stationary sequence, if Sn/Bn --> g[mu] for some 1/p-regularly varying sequence and some non-denegerate strictly p-stable law [mu]. The case 0 < p < 2 is investigated in detail and simplified necessary and sufficient conditions are given. The conditions consist of a mixing condition and polynomial large deviations for each tail (with a minor additional condition for p = 1). Methods of proving such large deviation results are discussed for [psi]-mixing, m-dependent, [phi]-mixing and associated sequences.