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On considère deux processus standards, à valeurs respectivement dans et et vérifiant l’hypothèse de H. Kunita et T. Watanabe. On donne une condition nécessaire et suffisante pour qu’une fonction séparément excessive pour ces deux processus et intégrable par rapport à une mesure de référence admette une représentation unique du type
où est une mesure sur le produit des compactifiés de Martin de et .
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