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arXiv:1507.06790 [math.PR]AbstractReferencesReviewsResources

The strong renewal theorem with infinite mean via local large deviations

R. A. Doney

Published 2015-07-24Version 1

A necessary and sufficient condition is established for an asymptotically stable random walk to satisfy the strong renewal theorem. This result is valid for all alpha in (0, 1), thus completing a result for alpha in (1/2, 1) which was proved in the 1963 paper of Garsia and Lamperti [6].

Comments: 21 pages
Categories: math.PR
Subjects: 60K05, 60F10
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