Extension du théorème de Cameron--Martin aux translations aléatoires
type: Dataset
description: Let G be a Gaussian vector taking its values in a separable Fréchet space E. We denote by $\gamma$ its law and by $(H,\Vert\!\cdot\!\Vert)$ its reproducing Hilbert space. Moreover, let X be an E-valued random vector of law $\mu$. In the first section, we prove that if $\mu$ is absolutely continuous relative to $\gamma$, then there exist necessarily a Gaussian vector $G'$ of law $\gamma$ and an H-valued random vector Z such that $G' + Z$ has the law $\mu$ of X. This fact is a direct consequence of concentration properties of Gaussian vectors and, in some sense, it is an unexpected achievement of a part of the Cameron--Martin theorem. In the second section, using the classical Cameron--Martin theorem and rotation invariance properties of Gaussian probabilities, we show that, in many situations, such a condition is sufficient for $\mu$ being absolutely continuous relative to $\gamma$.
landing page: 0091-1798
keyword: 60g15--60g30--28d05
keyword: absolue-continuite
keyword: absolute-continuity
keyword: cameron--martin-theorem
keyword: gaussian-probability
keyword: infoeu-reposemanticsarticle
keyword: journal-articles
keyword: mathmath-prmathematics-mathprobability-mathpr
keyword: probabilite-gaussienne
keyword: theoreme-de-cameron--martin
issued: 2026-05-08T18:10:58.961488
modified: 2026-05-08T18:10:58.961492
language: fr
contact point: Organization
  fn: CCSD

test_moissonnage_selune
type: Agent

Extension du théorème de Cameron--Martin aux translations aléatoires
type: Distribution
format: HTML
access URL: https://hal.science/hal-00089066
issued: 2026-05-08T18:10:58.963066
modified: 2026-05-08T18:10:58.941779