Stability of higher order eigenvalues in dimension one

Jordan Serres

doi:10.1016/j.spa.2022.10.013

Stability of higher order eigenvalues in dimension one

Jordan Serres

Université de Toulouse

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

Résumé

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 the Jacobi process).

langue originale	Anglais
Pages (de - à)	459-484
Nombre de pages	26
journal	Stochastic Processes and their Applications
Volume	155
Les DOIs	https://doi.org/10.1016/j.spa.2022.10.013
état	Publié - 1 janv. 2023
Modification externe	Oui

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10.1016/j.spa.2022.10.013

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title = "Stability of higher order eigenvalues in dimension one",

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 the Jacobi process).",

keywords = "Markov diffusion, Poincar{\'e} inequalities, Spectral analysis, Stein's method",

author = "Jordan Serres",

note = "Publisher Copyright: {\textcopyright} 2022 Elsevier B.V.",

year = "2023",

month = jan,

day = "1",

doi = "10.1016/j.spa.2022.10.013",

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T1 - Stability of higher order eigenvalues in dimension one

AU - Serres, Jordan

PY - 2023/1/1

Y1 - 2023/1/1

N2 - 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 the Jacobi process).

AB - 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 the Jacobi process).

KW - Markov diffusion

KW - Poincaré inequalities

KW - Spectral analysis

KW - Stein's method

UR - https://www.scopus.com/pages/publications/85141917146

U2 - 10.1016/j.spa.2022.10.013

DO - 10.1016/j.spa.2022.10.013

M3 - Article

AN - SCOPUS:85141917146

SN - 0304-4149

VL - 155

SP - 459

EP - 484

JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

ER -

Stability of higher order eigenvalues in dimension one

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