An ergodic diffusion with unbounded inward and outward drift

TL;DR

This paper explores conditions under which an ergodic diffusion process can have unbounded inward and outward drift components, challenging traditional assumptions about drift boundedness for ergodicity.

Contribution

It demonstrates that ergodicity can occur despite unbounded drift fields, using stochastic and numerical methods to analyze such diffusions.

Findings

Ergodic diffusion can have unbounded outward drift.

Numerical methods support theoretical findings.

Challenging the assumption that bounded drift is necessary for ergodicity.

Abstract

It is argued that a diffusion may be ergodic even though the drift field has unbounded outward-directed parts. The discussion employs stochastic and numerical methods.