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Under non-global Lipschitz condition, Euler Explicit method fails to convergestrongly to the exact solution, while Euler implicit method converges butrequires much computational efforts. Tamed scheme was first introduced in [2]to overcome this failure of the standard explicit method. This technique isextended to SDEs driven by Poisson jump in [3] where several schemes wereanalyzed. In this work, we investigate their nonlinear stability undernon-global Lipschitz and their linear stability. Numerical simulations tosustain the theoretical results are also provided.

Stability of the semi-tamed and tamed Euler schemes for stochastic differential equations with jumps under non-global Lipschitz condition