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              <p>Ce document étudie des limites d'échelle de chaînes de Markov ayant une dérive discontinue. Alors que beaucoup de travaux sur le sujet supposent que la dérive est continue, nous montrons que cette condition n'est pas nécessaire pour obtenir une limite déterministe. Nous montrons que sous des hypothèses faibles, un passage à l'échelle d'une chaîne de Markov peut être vu comme un algorithme d'approximation stochastique à pas constant, qui converge vers l'ensemble des solutions d'une inclusion différentielle. Cette inclusion est obtenue à partir d'une convexification de la dérive du processus initial. Cette méthode est générique et permet de calculer la région de stabilité de nombreux systèmes stochastique, en étudiant leur limite fluide. Elle permet aussi d'étendre les techniques d'approximation champ moyen à des systèmes où les discontinuités apparaissent naturellement, comme des réseaux de files d'attente ou des systèmes contrôlés par une politique à seuil.</p>
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