TY - JOUR
T1 - On series of discrete random variables, 1
T2 - Real trinomial distributions with fixed probabilities
AU - Deshouillers, Jean Marc
AU - Freiman, Gregory A.
AU - Moran, William
PY - 1999
Y1 - 1999
N2 - This paper begins the study of the local limit behaviour of triangular arrays of independent random variables (ζn,k)1≤k≤n where the law of ζn,k depends on on n. We consider the case when ζn,1 takes three integral values 0 < a1(n) < a2(n) with respective probabilities p0,p1,p2 which do not depend on n. We show three types of limit behaviours for the sequence of r. v. ηn = ζn,1 + ⋯ + ζn,n, according as a2(n)/gcd(a1(n), a2(n)) tends to infinity slower, quicker or at the same speed as √n.
AB - This paper begins the study of the local limit behaviour of triangular arrays of independent random variables (ζn,k)1≤k≤n where the law of ζn,k depends on on n. We consider the case when ζn,1 takes three integral values 0 < a1(n) < a2(n) with respective probabilities p0,p1,p2 which do not depend on n. We show three types of limit behaviours for the sequence of r. v. ηn = ζn,1 + ⋯ + ζn,n, according as a2(n)/gcd(a1(n), a2(n)) tends to infinity slower, quicker or at the same speed as √n.
KW - Characteristic function
KW - Circle method
KW - Local limit theorems
KW - Number theoretic methods
KW - Sums of discrete random variables
UR - http://www.scopus.com/inward/record.url?scp=0010170469&partnerID=8YFLogxK
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AN - SCOPUS:0010170469
SN - 0303-1179
VL - 258
SP - 411
EP - 423
JO - Asterisque
JF - Asterisque
ER -