Convergence of numerical solutions to stochastic delay differential equations with jumps
Convergence of numerical solutions to stochastic delay differential equations with jumps
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DOI：
10.1016/j.amc.2005.02.017
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发表时间：
2006
期刊：
影响因子：
--
通讯作者：
Ronghua Li;Hongbing Meng;Yonghong Dai
中科院分区：
文献类型：
--
作者：
Ronghua Li;Hongbing Meng;Yonghong Dai
研究了一类带跳变的随机时滞微分方程。SDDEJs很难得到显式的解。需要适当的数值近似格式，如欧拉格式，以在实践中应用SDDEJs或研究其性质。在较弱的线性增长条件和全局Lipschitz条件下，证明了SDDEJs的Euler逼近解收敛于解析解。给出了一个例子来说明。
This paper studies a class of stochastic delay differential equations with jumps (SDDEJs). Explicit solutions can hardly be obtained for the SDDEJs. Appropriate numerical approximation schemes such as the Euler scheme are needed to apply SDDEJs in practice or to study their properties. In this paper, it is proved that the Euler approximation solutions converge to the analytic solution for SDDEJs under weaker conditions than the linear growth condition and global Lipschitz condition. An example is given for illustration.