Large deviations for hierarchical systems of interacting jump processes
The authors study the limiting behaviour of some Markovian systems of jump processes obeying a two-level hierarchy interaction, which in the limit, as the number of subsystems grows to infinity, satisfy a McKean-Vlasov type equation. For the corresponding empirical distribution, a large deviation upper bound is obtained and the associated rate function is shown to admit two representations, a Lagrangian and a nonvariational (integral) one. Moreover, the admissible paths for the weak solution of the McKean-Vlasov equation are proven to obey some strong differentiability properties. Application to a certain epidemic model is also discussed.
scientific article; zbMATH DE number 1138554