Does the Convex Order Between the Distributions of Linear Functionals Imply the Convex Order Between the Probability Distributions Over $\mathbb R^d$?
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866908581770559488 |
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| author | Pinelis, Iosif |
| author_facet | Pinelis, Iosif |
| contents | It is shown that the convex order between the distributions of linear functionals does not imply the convex order between the probability distributions over $\mathbb R^d$ if $d\ge2$. This stands in contrast with the well-known fact that any probability distribution in $\mathbb R^d$, for any $d\ge1$, is determined by the corresponding distributions of linear functionals. By duality, it follows that, for any $d\ge2$, not all convex functions from $\mathbb R^d$ to $\mathbb R$ can be represented as the limits of sums $\sum_{i=1}^k g_i\circ \ell_i$ of convex functions $g_i$ of linear functionals $\ell_i$ on $\mathbb R^d$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_04269 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Does the Convex Order Between the Distributions of Linear Functionals Imply the Convex Order Between the Probability Distributions Over $\mathbb R^d$? Pinelis, Iosif Probability 60E15 It is shown that the convex order between the distributions of linear functionals does not imply the convex order between the probability distributions over $\mathbb R^d$ if $d\ge2$. This stands in contrast with the well-known fact that any probability distribution in $\mathbb R^d$, for any $d\ge1$, is determined by the corresponding distributions of linear functionals. By duality, it follows that, for any $d\ge2$, not all convex functions from $\mathbb R^d$ to $\mathbb R$ can be represented as the limits of sums $\sum_{i=1}^k g_i\circ \ell_i$ of convex functions $g_i$ of linear functionals $\ell_i$ on $\mathbb R^d$. |
| title | Does the Convex Order Between the Distributions of Linear Functionals Imply the Convex Order Between the Probability Distributions Over $\mathbb R^d$? |
| topic | Probability 60E15 |
| url | https://arxiv.org/abs/2510.04269 |