Quantitative estimates for Lévy driven SDEs with different drifts and applications

By partly invoking the refined basic coupling for the Lévy process, we establish quantitative estimates of distributions associated with two Lévy driven SDEs with different drifts, which are partially dissipative. This quantitative result is powerful not only to investigate the exponentially contractive property of distributions corresponding to partially dissipative McKean-Vlasov SDEs with jumps but also to handle the long time behavior of time-inhomogeneous SDEs with jumps. Our approach also works very well for two Lévy driven SDEs with different drift terms, which satisfy monotone and Lyapunov conditions. As important applications of the result in this aspect, under monotone and Lyapunov conditions, we obtain succinctly the exponential decay and the locally exponential contractivity as well as the exponential ergodicity for McKean-Vlasov SDEs driven by Lévy noises.