Transcritical bifurcation for the conditional distribution of a diffusion process

TL;DR

This paper investigates a class of absorbed diffusion processes where the conditional distribution undergoes a transcritical bifurcation, using quasi-stationary distributions to analyze the bifurcation behavior.

Contribution

It introduces a simple model framework for absorbed diffusion processes with bifurcation phenomena in their conditional laws, based on quasi-stationary distribution analysis.

Findings

Identification of transcritical bifurcation in conditional distributions

Characterization of quasi-stationary distributions for reducible processes

Insights into bifurcation behavior in diffusion models

Abstract

In this article, we describe a simple class of models of absorbed diffusion processes with parameter, whose conditional law exhibits a transcritical bifurcation. Our proofs are based on the description of the set of quasi-stationary distributions for general two-clusters reducible processes.