Tails of Polynomials of Random Variables and Stable Limits for Nonconventional Sums

First, we obtain decay rates of probabilities of tails of polynomials in several independent random variables with heavy tails. Then we derive stable limit theorems for sums of the form where F is a polynomial, is either or ni and is a sequence of independent identically distributed random variables with heavy tails. Our results can be viewed as an extension to the heavy tails case of the nonconventional functional central limit theorem from Kifer and Varadhan (Ann Probab 42:649-688, 2014).