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Let O the basin of attraction of the unique stable equilibrium of a dynamicalsystem, which is the law of large numbers limit of a Poissonian SDE. Weconsider the law of the exit point from O of that Poissonian SDE. We adapt theapproach of M. Day (1990) for the same problem for a Brownian SDE. For thatpurpose, we will use the Large deviation for the Poissonian SDE reflected atthe boundary of O studied in our recent work Pardoux and Samegni (2018).

Large Deviations of the Exit Measure through a Characteristic Boundary for a Poisson driven SDE