Minimal conditions in p-stable limit theorems — II

A p-stable limit theorem holds for partial sums Sn of a stationary sequence, if SnBn → gμ for some 1/p-regularly varying sequence and some non-denegerate strictly p-stable law μ. 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). s of proving such large deviation results are discussed for ψ-mixing, m-dependent, φ-mixing and associated sequences.