English

The discrete renewal theorem with bounded interevent times

Probability 2025-10-17 v1

Abstract

The purpose of this note is to prove the celebrated Discrete Renewal Theorem in a common special case. We use only very elementary methods from real analysis, rather than markov chain theory, complex analysis, or generating functions. Provided is an introduction to a 1d discrete renewal process via a board game example, our proof the discrete renewal theorem, as well as background and history of the Erd\v{o}s-Feller-Pollard Theorem.

Keywords

Cite

@article{arxiv.2510.14020,
  title  = {The discrete renewal theorem with bounded interevent times},
  author = {Rohan Shenoy},
  journal= {arXiv preprint arXiv:2510.14020},
  year   = {2025}
}