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

Research output: Contribution to journal › Article › peer-review

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).

Original language	English
Pages (from-to)	459-484
Number of pages	26
Journal	Stochastic Processes and their Applications
Volume	155
DOIs	https://doi.org/10.1016/j.spa.2022.10.013
Publication status	Published - 1 Jan 2023
Externally published	Yes

Keywords

Markov diffusion
Poincaré inequalities
Spectral analysis
Stein's method

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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",

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year = "2023",

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day = "1",

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

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AU - Serres, Jordan

PY - 2023/1/1

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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

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

Abstract

Keywords

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