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

2015/10/20 by Antoine Tambue, Tambue, Antoine, Jean Daniel Mukam +1
Earth and Planetary Sciences · Economics, Econometrics and Finance · Engineering · #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Meteorological Phenomena and Simulations #Numerical Analysis (math.NA) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1510.06067

openalex publication_date 2015/10/20 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/01

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.

Citations

• Numerical methods for nonlinear stochastic differential equations with jumps

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