Large Deviation Principle for a Two-Time-Scale Mckean–Vlasov Model With Jumps

This work focuses on the large deviation principle for a two-time-scale McKean–Vlasov system with jumps. Based on the variational framework of the McKean–Vlasov system with jumps, it is turned into weak convergence for the controlled system. Unlike general two-timescale system, the controlled McKean–Vlasov system is related to the law of the original system, which causes difficulties in qualitative analysis. In solving this issue, employing asymptotics of the original system and a Khasminskii-type averaging principle together is efficient. Finally, it is shown that the limit is related to the Dirac measure of the solution to the ordinary differential equation.