The strong renewal theorem with infinite mean via local large deviations

2015/07/24 by Doney, R. A.
#60F10 #60K05 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1507.06790

Abstract

A necessary and sufficient condition is established for an asymptotically stable renewal process 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]. This paper is superseded by arXiv:1612.07635.

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