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

Franziska Kühn and René L. Schilling

Stochastic Processes and their Applications, 2019, vol. 129, issue 8, 2654-2680

Abstract: Consider the following stochastic differential equation (SDE) dXt=b(t,Xt−)dt+dLt,X0=x,driven by a d-dimensional Lévy process (Lt)t≥0. We establish conditions on the Lévy 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 Lévy 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 Lévy processes, e.g. isotropic stable, relativistic stable, tempered stable and layered stable.

Keywords: Euler–Maruyama approximation; Stochastic differential equation; Strong convergence (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:129:y:2019:i:8:p:2654-2680

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DOI: 10.1016/j.spa.2018.07.018

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