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. En-conséquence, En plus, cette méthode est utilisée pour montrer l'existence de solutions du processus de rafle perturbé avec des conditions initiales non locales. Latroisì eme méthode est la technique de régularisation de Moreau-Yosida qui consistè a approcher une inclusion différentielle donnée par une pénalisée, en fonction d'un paramètre positif, puis passeràpasserà la limite lorsque le paramètre tend vers zéro. Cette méthode est utilisée pour traiter les processus de rafle dépendants de l'´ etat régis par des ensembles uniformement sous-lisses, Finalement, dans latroisì eme partie Deuxì eme partie du Chapitre 8 et Chapitre 9), on fournit des caractérisations des paires de Lyapunov faibles et l'invariance faible pour le processus de rafle perturbé avec des ensembles uniformement sous-lisses