Abstract
Necessary and sufficient conditions are given for multidimensional p – stable limit theorems (i.e. theorems on convergence of normalized partial sums of a stationary sequence of random vectors to a non-degenerate strictly p-stable limiting law μ with -regularly varying normalizing sequence ). It is proved that similarly as in the one-dimensional case the conditions for consist of two parts: one responsible for (very weak) mixing properties and another, describing asymptotics of probabilities of large deviations (with a minor additional condition for ). The paper focuses on effective methods of proving such large deviation results
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