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arXiv · 1510.06067

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

Antoine Tambue·Jean Daniel Mukam
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Abstract

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.

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Antoine Tambue, Jean Daniel Mukam. 2015-10-20. Stability of the semi-tamed and tamed Euler schemes for stochastic differential equations with jumps under non-global Lipschitz condition. https://arxiv.org/abs/1510.06067

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