Well-posedness and approximation of some one-dimensional Lévy-driven non-linear SDEs

In this article, we are interested in the strong well-posedness together with numerical approximation of some one-dimensional stochastic differential equations a non-linear drift, sense McKean–Vlasov, driven by spectrally-positive Lévy process and Brownian motion. We provide criteria for existence solutions under non-Lipschitz conditions Yamada–Watanabe type without non-degeneracy assumption following approach developed Li Mytnik (2011). The convergence rate propagation chaos associated particle system corresponding Euler–Maruyama scheme also investigated. particular, exhibits an interplay between regularity coefficients order singularity measure around zero.