Anderson, Kevin K. ; Athreya, Krishna B.
(1988)
*A strong renewal theorem for generalized renewal functions in the infinite mean case*
Probability Theory and Related Fields, 77
(4).
pp. 471-479.
ISSN 0178-8051

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Official URL: http://www.springerlink.com/content/ln363lv1786454...

Related URL: http://dx.doi.org/10.1007/BF00959611

## Abstract

Let F(x) be a nonarithmetic c.d.f. on (0, ∞) such that 1 -F(x)=x. α L(x), where L(x) is slowly varying and 0 ≤ α ≤ 1. Let a(x) be regularly varying with exponent β≥1. A strong renewal theorem (of Blackwell type) for generalized renewal functions of the form G(t) ≡ ∑ ^{∞}_{n=0}a(n)F^{n}(t) is proved here, thus extending the recent work of Embrechts, Maejima and Omey [1] and that of Erickson [4].

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ID Code: | 1157 |

Deposited On: | 05 Oct 2010 12:51 |

Last Modified: | 12 May 2011 10:02 |

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