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We consider “nonconventional” averaging setup in the form , where , is either a stochastic process or a dynamical system with sufficiently fast mixing while , and , grow faster than linearly. We show that the properly normalized error term in the “nonconventional” averaging principle is asymptotically Gaussian.
Dans cet article, nous étudions les résultats de grandes déviations associés au couple , solution de l’E.D.S. interprétée au sens d’Itô :avec des conditions assez générales sur les coefficients et dans les deux cas suivants :Premier cas : est indépendant du mouvement brownien et satisfait à un principe de grandes déviations ;Deuxième cas : est un processus markovien avec un nombre fini d’états vérifiantuniformément dans pourvu que .Ces résultats sont des extensions de ceux de Bezuidenhout...
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