Abstract
Nous determinons le comportement asymptotique en temps long d’une diffusion relativiste a valeurs dans le fibre tangent unitaire d’un espace de Robertson–Walker. On montre en particulier qu’au voisinage du temps d’explosion de la diffusion, sa projection sur la variete de base converge presque surement vers un point aleatoire de la frontiere causale et nous decrivons le comportement du vecteur tangent au voisinage de ce point limite.
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