Convex comparison of Gaussian mixtures

Benjamin Jourdain; Gilles Pagès

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arXiv · 2410.07958

Convex comparison of Gaussian mixtures

Benjamin Jourdain·Gilles Pagès

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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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Benjamin Jourdain, Gilles Pagès. 2024-10-10. Convex comparison of Gaussian mixtures. https://arxiv.org/abs/2410.07958

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