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.
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