Stability of higher order eigenvalues in dimension one

TL;DR

This paper investigates how the eigenvalues of the generator of one-dimensional reversible diffusion processes remain stable under perturbations, using Stein's method across various distributions.

Contribution

It introduces a stability analysis framework for eigenvalues of diffusion generators, applying Stein's method to specific distributions like Normal, Gamma, and Beta.

Findings

Eigenvalues exhibit stability under certain conditions.

Results apply to Normal, Gamma, and Beta distributions.

Stein's method effectively analyzes eigenvalue stability.

Abstract

We study stability of the eigenvalues of the generator of a one dimensional reversible diffusion process satisfying some natural conditions. The proof is based on Stein's method. In particular, these results are applied to the Normal distribution (via the Ornstein-Uhlenbeck process), to Gamma distributions (via the Laguerre process) and to Beta distributions (via Jacobi process).