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A Renewal Theorem of Blackwell Type

Paul Embrechts, Makoto Maejima and Edward Omey
The Annals of Probability
Vol. 12, No. 2 (May, 1984), pp. 561-570
Stable URL: http://www.jstor.org/stable/2243487
Page Count: 10
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A Renewal Theorem of Blackwell Type
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Abstract

Suppose {X1, X2, ⋯} are i.i.d. random variables with finite mean $0 < E(X_1) < \infty$. If Sn stands for the nth partial sum, and {a(n)}n is a sequence of nonnegative numbers, then G(x) = ∑∞ n = 0 a(n)P{Sn ≤ x} is a generalized renewal measure. We investigate the behaviour of G(x + h) - G(x) as x → ∞ for {a(n)}n regularly varying.

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