TY - JOUR
T1 - Tails of Polynomials of Random Variables and Stable Limits for Nonconventional Sums
AU - Kifer, Yuri
AU - Varadhan, S. R.S.
N1 - Publisher Copyright:
© 2016, Springer Science+Business Media New York.
PY - 2017/2/1
Y1 - 2017/2/1
N2 - 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 ∑Nt≥n≥1F(Xq1(n),…,Xqℓ(n)) where F is a polynomial, qi(n) is either n- 1 + i or ni and Xn, n≥ 0 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).
AB - 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 ∑Nt≥n≥1F(Xq1(n),…,Xqℓ(n)) where F is a polynomial, qi(n) is either n- 1 + i or ni and Xn, n≥ 0 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).
KW - Heavy tails
KW - Levi process
KW - Limit theorems
KW - Nonconventional sums
KW - Stable distributions
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U2 - 10.1007/s10955-016-1561-5
DO - 10.1007/s10955-016-1561-5
M3 - Article
AN - SCOPUS:84975110718
SN - 0022-4715
VL - 166
SP - 575
EP - 608
JO - Journal of Statistical Physics
JF - Journal of Statistical Physics
IS - 3-4
ER -