English

Quantitative exponential bounds for the renewal theorem with spread-out distributions

Probability 2016-12-01 v3

Abstract

We establish explicit exponential convergence estimates for the renewal theorem, in terms of a uniform component of the inter arrival distribution, of its Laplace transform which is assumed finite on a positive interval, and of the Laplace transform of some related random variable. Our proof is based on a coupling construction relying on discrete-time Markovian structures that underly the renewal processes and on Lyapunov-Doeblin type arguments.

Keywords

Cite

@article{arxiv.1504.06184,
  title  = {Quantitative exponential bounds for the renewal theorem with spread-out distributions},
  author = {J. -B Bardet and A Christen and J Fontbona},
  journal= {arXiv preprint arXiv:1504.06184},
  year   = {2016}
}

Comments

Accepted for publication in Markov Processes and Related Fields

R2 v1 2026-06-22T09:21:20.172Z