分野別セミナー

The aim of this work is to investigate averaging principle and large deviations for a slow-fast McKean-Vlasov system with jump processes. Firstly, the averaging principle can be established via the time discretization techniques. Based on the variational representation of the McKean-Vlasov system with jumps, the large deviation is turned into weak convergence for the controlled system. Different from general the slow-fast system, the controlled McKean-Vlasov system is related to the distribution of the original system. Due to this particularity, the asymptotics of the original system and a Khasminskii type averaging principle will be employed together in the analysis. Finally, it is shown that the limit is related to the Dirac measure of the solution to the ordinary differential equation.