English

The strong renewal theorem with infinite mean via local large deviations

Probability 2017-01-10 v3

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 This paper is superseded by arXiv:1612.07635.

Cite

@article{arxiv.1507.06790,
  title  = {The strong renewal theorem with infinite mean via local large deviations},
  author = {R. A. Doney},
  journal= {arXiv preprint arXiv:1507.06790},
  year   = {2017}
}

Comments

19 pages

R2 v1 2026-06-22T10:17:44.877Z