TY - JOUR
T1 - Estimates for interval probabilities of the sums of random variables with locally subexponential distributions
AU - Shneer, V.
PY - 2006
Y1 - 2006
N2 - Let {i} i=1 be a sequence of independent identically distributed nonnegative random variables, S n = ¿1 + ¿ +¿n. Let ¿ = (0, T] and x + ¿ = (x, x + T]. We study the ratios of the probabilities P(S n e x + ¿)/P(¿ 1 e x + ¿) for all n and x. The estimates uniform in x for these ratios are known for the so-called ¿-subexponential distributions. Here we improve these estimates for two subclasses of ¿-subexponential distributions; one of them is a generalization of the well-known class LC to the case of the interval (0, T] with an arbitrary T = 8. Also, a characterization of the class LC is given.
AB - Let {i} i=1 be a sequence of independent identically distributed nonnegative random variables, S n = ¿1 + ¿ +¿n. Let ¿ = (0, T] and x + ¿ = (x, x + T]. We study the ratios of the probabilities P(S n e x + ¿)/P(¿ 1 e x + ¿) for all n and x. The estimates uniform in x for these ratios are known for the so-called ¿-subexponential distributions. Here we improve these estimates for two subclasses of ¿-subexponential distributions; one of them is a generalization of the well-known class LC to the case of the interval (0, T] with an arbitrary T = 8. Also, a characterization of the class LC is given.
U2 - 10.1007/s11202-006-0088-4
DO - 10.1007/s11202-006-0088-4
M3 - Article
SN - 1055-1344
VL - 47
SP - 779
EP - 786
JO - Siberian Advances in Mathematics
JF - Siberian Advances in Mathematics
IS - 4
ER -