Stability of higher order eigenvalues in dimension one (Q2105082)

The paper studies the 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. After a detailed introduction, the author in Section 2 explicitly describes the space of normalized probability distributions on which the stability result holds. The following section contains approximate integration by parts formulas. Starting from Section 4, 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 the Jacobi process).