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

Etienne Pardoux; Brice Samegni-Kepgnou

doi:10.1051/ps/2019031

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arXiv · 1808.04991

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

Etienne Pardoux·Brice Samegni-Kepgnou

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Abstract

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

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Etienne Pardoux, Brice Samegni-Kepgnou. 2018-08-15. Large Deviations of the Exit Measure through a Characteristic Boundary for a Poisson driven SDE. https://doi.org/10.1051/ps%2F2019031

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