A simple proof of Blackwell's renewal theorem by mapping to integers

TL;DR

This paper offers a straightforward proof of Blackwell's renewal theorem by transforming a general point process into a deterministic process, providing clearer understanding of the theorem's mechanics.

Contribution

It introduces a novel proof technique for the renewal theorem through a bijection to a deterministic process, enhancing conceptual clarity.

Findings

Simplifies the proof of Blackwell's renewal theorem

Provides new insights into the theorem's underlying mechanisms

Establishes a bijection between stochastic and deterministic processes

Abstract

This paper presents a new proof of the renewal theorem by bijecting a general point process to a deterministic one (where the time between events is always fixed). It also provides insight into the workings of the renewal theorem.