Strong convergence rates for backward Euler on a class of nonlinear jump-diffusion problems
Strong convergence rates for backward Euler on a class of nonlinear jump-diffusion problems
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DOI：
10.1016/j.cam.2006.03.039
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发表时间：
2007-08
影响因子：
2.4
通讯作者：
D. Higham;P. Kloeden
中科院分区：
文献类型：
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作者：
D. Higham;P. Kloeden
我们通过允许随机微分方程 (SDE) 中泊松驱动的跳跃来推广基于隐式欧拉方法的当前最佳强收敛率理论。更准确地说，我们表明，在漂移系数的单侧 Lipschitz 和多项式增长条件以及扩散和跳跃系数的全局 Lipschitz 条件下，向后欧拉的三个变体以二分之一的强阶收敛。该分析利用了后向和显式欧拉方法之间的关系。
We generalise the current theory of optimal strong convergence rates for implicit Euler-based methods by allowing for Poisson-driven jumps in a stochastic differential equation (SDE). More precisely, we show that under one-sided Lipschitz and polynomial growth conditions on the drift coefficient and global Lipschitz conditions on the diffusion and jump coefficients, three variants of backward Euler converge with strong order of one half. The analysis exploits a relation between the backward and explicit Euler methods.