Tails of polynomials of random variables and stable limits for nonconventional sums

arXiv1504.04213MaRDI QIDQ6260926

S. R. S. Varadhan, Yuri Kifer

Publication date: 16 April 2015

Abstract: We obtain first decay rates of probabilities of tails of multivariate polynomials built on independent random variables with heavy tails. Then we derive stable limit theorems for nonconventional sums of the form $su{m}_{Ntgeqngeq1}F(X(q_1(n)),...,X(q_{e}ll(n)))$ where $F$ is a polynomial, $1leq{q}_1(n)<cdots<q_{e}ll(n)$ are integer valued increasing functions satisfying certain conditions and $X(n),,ngeq0$ is a sequence of independent random variables with heavy tails.

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