Stability of the semi-tamed and tamed Euler schemes for stochastic differential equations with jumps under non-global Lipschitz condition
For researchers working on numerical methods for SDEs with jumps, this work extends stability analysis to non-global Lipschitz settings, but it is incremental as it builds on existing tamed schemes.
The paper analyzes the nonlinear and linear stability of semi-tamed and tamed Euler schemes for stochastic differential equations with jumps under non-global Lipschitz conditions, providing numerical simulations to support the theoretical results.
Under non-global Lipschitz condition, Euler Explicit method fails to converge strongly to the exact solution, while Euler implicit method converges but requires much computational efforts. Tamed scheme was first introduced in [2] to overcome this failure of the standard explicit method. This technique is extended to SDEs driven by Poisson jump in [3] where several schemes were analyzed. In this work, we investigate their nonlinear stability under non-global Lipschitz and their linear stability. Numerical simulations to sustain the theoretical results are also provided.