Convex comparison of Gaussian mixtures

Benjamin Jourdain; Gilles Pagès

doi:10.1016/j.jmva.2025.105448

Convex comparison of Gaussian mixtures

Benjamin Jourdain, Gilles Pagès

Sorbonne Université

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

Abstract

Motivated by the study of the propagation of convexity by semi-groups of stochastic differential equations and convex comparison between the distributions of solutions of two such equations, we study the comparison for the convex order between a Gaussian distribution and a Gaussian mixture. We give and discuss intrinsic necessary and sufficient conditions for convex ordering. On the examples that we have worked out, the two conditions appear to be closely related.

Original language	English
Article number	105448
Journal	Journal of Multivariate Analysis
Volume	209
DOIs	https://doi.org/10.1016/j.jmva.2025.105448
Publication status	Published - 1 Sept 2025

Keywords

Convex order
Covariance matrices
Gaussian mixtures

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10.1016/j.jmva.2025.105448

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title = "Convex comparison of Gaussian mixtures",

abstract = "Motivated by the study of the propagation of convexity by semi-groups of stochastic differential equations and convex comparison between the distributions of solutions of two such equations, we study the comparison for the convex order between a Gaussian distribution and a Gaussian mixture. We give and discuss intrinsic necessary and sufficient conditions for convex ordering. On the examples that we have worked out, the two conditions appear to be closely related.",

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AU - Pagès, Gilles

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N2 - Motivated by the study of the propagation of convexity by semi-groups of stochastic differential equations and convex comparison between the distributions of solutions of two such equations, we study the comparison for the convex order between a Gaussian distribution and a Gaussian mixture. We give and discuss intrinsic necessary and sufficient conditions for convex ordering. On the examples that we have worked out, the two conditions appear to be closely related.

AB - Motivated by the study of the propagation of convexity by semi-groups of stochastic differential equations and convex comparison between the distributions of solutions of two such equations, we study the comparison for the convex order between a Gaussian distribution and a Gaussian mixture. We give and discuss intrinsic necessary and sufficient conditions for convex ordering. On the examples that we have worked out, the two conditions appear to be closely related.

KW - Convex order

KW - Covariance matrices

KW - Gaussian mixtures

UR - https://www.scopus.com/pages/publications/105004580649

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DO - 10.1016/j.jmva.2025.105448

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SN - 0047-259X

VL - 209

JO - Journal of Multivariate Analysis

JF - Journal of Multivariate Analysis

M1 - 105448

ER -

Convex comparison of Gaussian mixtures

Abstract

Keywords

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