Abstract
We investigate the large deviations principle from the McKean–Vlasov limit for a collection of jump processes obeying a two-level hierarchy interaction. A large deviation upper bound is derived and it is shown that the associated rate function admits a Lagrangian representation as well as a nonvariational one. Moreover, it is proved that the admissible paths for the weak solution of the McKean–Vlasov equation enjoy certain strong differentiability properties.
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Djehiche, B., Schied, A. Large Deviations for Hierarchical Systems of Interacting Jump Processes. Journal of Theoretical Probability 11, 1–24 (1998). https://doi.org/10.1023/A:1021690707556
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DOI: https://doi.org/10.1023/A:1021690707556