Form discrete- to continuous-time ergodic theorems

TL;DR

This paper develops methods to convert discrete-time ergodic theorems into continuous-time versions, providing simpler proofs, refinements, and new results in ergodic theory.

Contribution

It introduces a novel approach for deriving continuous-time ergodic theorems from discrete-time counterparts, including new theoretical results.

Findings

Simplified proofs of known ergodic theorems

Refinements of existing results

New continuous-time ergodic theorems

Abstract

We introduce methods that allow to derive continuous-time versions of various discrete-time ergodic theorems. We then illustrate these methods by giving simple proofs and refinements of some known results as well as establishing new results of interest.