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

被引:28
作者
Kuehn, Franziska [1 ]
Schilling, Rene L. [2 ]
机构
[1] Univ Paul Sabatier III Toulouse, Inst Math Toulouse, 118 Route Narbonne, F-31062 Toulouse, France
[2] Tech Univ Dresden, Fachrichtung Math, Inst Math Stochast, D-01062 Dresden, Germany
关键词
Euler-Maruyama approximation; Stochastic differential equation; Strong convergence; EXISTENCE;
D O I
10.1016/j.spa.2018.07.018
中图分类号
O21 [概率论与数理统计]; C8 [统计学];
学科分类号
020208 ; 070103 ; 0714 ;
摘要
Consider the following stochastic differential equation (SDE) dX(t) = b(t, Xt-)dt + dL(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. (C) 2018 Elsevier B.V. All rights reserved.
引用
收藏
页码:2654 / 2680
页数:27
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