Long time behaviour of 1/2 H\"older diffusion population processes

TL;DR

This paper studies the long-term behavior of H"older continuous diffusion processes on compact sets, showing they hit the boundary in finite time and establishing the existence of a quasi-stationary distribution.

Contribution

It provides new results on the boundary hitting times and quasi-stationary distributions for H"older diffusion processes, extending understanding of their long-term dynamics.

Findings

Processes hit the boundary in finite time

Existence of a quasi-stationary distribution

Behavior characterized on compact sets

Abstract

In this paper we investigate the long time behavior of a family of diffusion processes with H\"older continuous diffusion terms on a compact set, these process arise naturally in random approximations of an ODE. We will prove that these processes hit the boundary in finite time and prove the existence of a quasi-stationnary distribution