Access

You are not currently logged in.

Access your personal account or get JSTOR access through your library or other institution:

If You Use a Screen Reader

This content is available through Read Online (Free) program, which relies on page scans. Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.

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
Preview not available

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.

• 561
• 562
• 563
• 564
• 565
• 566
• 567
• 568
• 569
• 570