Abstract
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. © 2006 Springer Science+Business Media, Inc.
Original language | English |
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Pages (from-to) | 779-786 |
Number of pages | 8 |
Journal | Siberian Mathematical Journal |
Volume | 47 |
Issue number | 4 |
DOIs | |
Publication status | Published - Jul 2006 |
Keywords
- Estimates for interval probabilities
- Locally subexponential distribution
- Subexponential distribution
- Sums of random variables