Strong convergence of the Euler–Maruyama approximation for a class of Lévy-driven SDEs

By F. Kühn, René L. Schilling. Stochastic Processes and their Applications, 2017

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Abstract Consider the following stochastic differential equation (SDE) d X t = b ( t , X t − ) d t + d L t , X 0 = x , driven by a d -dimensional Levy process ( L t ) t ≥ 0 . We establish conditions on the Levy process and the drift coefficient b such that the Euler–Maruyama approximation converges strongly to a solution of the SDE with an explicitly given rate. The convergence rate depends on the regularity of b and the behaviour of the Levy measure at the origin. As a by-product of the proof, we obtain that the SDE has a pathwise unique solution. Our result covers many important examples of Levy processes, e.g. isotropic stable, relativistic stable, tempered stable and layered stable.

Subfields: Finance, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/a47996fad96c2868f71c83167b91aac959817360