带跳的非线性随机延迟微分方程的Split-step算法  

Split-Step Method for Nonlinear Stochastic Delay Differential Equation with Jumps

作　　者：裘贇辰 王臻臻[1] 秦衍[1] 

机构地区：[1]华东理工大学数学系,上海200237

出　　处：《华东理工大学学报（自然科学版）》2014年第6期810-816,共7页Journal of East China University of Science and Technology

摘　　要：研究了It意义下一类具有特殊情形的、带跳的非线性随机延迟微分方程的Split-step算法,证明了该算法在均值意义下以1.5阶矩一致收敛,在均方意义下以1阶矩一致收敛;得到了Split-step法均方稳定的条件,最后通过一些数值实例验证了算法的有效性。This paper discusses split-step algorithm for solving nonlinear stochastic delay differential equation with jumps in It6 sense. It is proved that the split-step method is uniformly convergent with order of 1.5 in the mean sense and order of 1 in the mean-square sense. The mean-square stable of the split-step method under some conditions is also obtained. Some numerical experiments are reported to testify the performance and effectiveness of this method in this paper.

关 键 词：泊松跳 数值解 均方稳定 一致收敛 

分 类 号：O13[理学—数学]