摘要
针对满足广义Khasminskii条件的由维纳过程和泊松随机测度驱动的自变量分段连续型随机微分方程(EPCASDEs),给出了Euler方法,广义Khasminskii条件比经典条件包容了更多的EPC.ASDEs.现有文献对该类方程的研究成果较少.针对EPCASDEs在广义Khasminskii条件下证明了全局解的存在唯一性,并研究了Euler方法的依概率收敛性.给出了数值算例支持主要结论.
In this paper,Euler method is introduced for equations with piecewise continuous arguments(EPCAs) driven by Wiener process and Poisson random measure under the generalized Khasminskii-type conditions which cover more classes of such equations than classical conditions.To our known,few results are presented to such equations in current literature.The main aims of this paper are to prove the existence of global solutions to such equations and then to investigate the convergence of the Euler method in probability under the Khasminskii-type conditions.Numerical example is given to show our results.
出处
《数学的实践与认识》
北大核心
2017年第1期236-246,共11页
Mathematics in Practice and Theory
基金
黑龙江省哲学社会科学研究规划项目"全面"两孩"政策下黑龙江人口的随机动态效应分析和对策研究"(16TJE01)
大庆市哲学社会科学规划研究项目"大庆产业转型模式的分析及其随机模型的构建"(DSGB2016095)
黑龙江八一农垦大学学成
引进人才科研启动计划(XDB2014-16)
黑龙江省大学生创新创业训练计划项目(201410223020)