A renewal theorem in the finitemean case
Author:
J. L. Geluk
Journal:
Proc. Amer. Math. Soc. 125 (1997), 34073413
MSC (1991):
Primary 60K05
MathSciNet review:
1403127
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Abstract: Let be a c.d.f. on such that is regularly varying with exponent . Then as , where is the renewal function associated with . Moreover similar estimates are given for distributions in the domain of attraction of the normal distribution and for the variance of The estimates improve earlier results of Teugels and Mohan.
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 Bingham, N.H., Goldie, C.M. and Teugels, J.L. (1987). Regular variation. Cambridge Univ. Press. MR 88i:26004
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 Erickson, K.B. (1970). Strong renewal theorems with infinite mean. Trans. Amer. Math. Soc. 151 263291. MR 42:3873
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Additional Information
J. L. Geluk
Affiliation:
Econometric Institute, Erasmus University Rotterdam, P.O. Box 1738, NL3000 DR Rotterdam, The Netherlands
Email:
jgeluk@few.eur.nl
DOI:
http://dx.doi.org/10.1090/S0002993997039555
PII:
S 00029939(97)039555
Keywords:
Renewal function,
regular variation,
key renewal theorem,
domain of attraction
Received by editor(s):
March 12, 1996
Received by editor(s) in revised form:
June 21, 1996
Communicated by:
Stanley Sawyer
Article copyright:
© Copyright 1997
American Mathematical Society
