非Lipschitz条件下带Poisson测度随机微分方程Euler方法的依概率收敛性  

The convergence of the Euler method in probability to stochastic differential equations with Poisson measure under the non-Lipschitz conditions

作　　者：于辉[1] 周晓琳[1] 李欣[1] 

机构地区：[1]黑龙江八一农垦大学理学院,黑龙江大庆163319

出　　处：《高师理科学刊》2015年第11期12-17,共6页Journal of Science of Teachers＇College and University

基　　金：黑龙江八一农垦大学学成;引进人才科研启动计划:随机微分方程的数值解法及其应用(XDB2014-16);黑龙江省大学生创新创业训练计划项目:木糖醇发酵的随机延迟微分方程模型分析(201410223020);黑龙江省教育厅科学技术研究面上项目(12521374);大庆市指导性科技计划项目:环境毒素对生物种群影响的随机模型研究

摘　　要：针对满足非Lipschitz条件的带Poisson测度的随机微分方程(SDEs),给出了Euler方法.非Lipschitz条件比经典条件包容了更多的SDEs,现有文献对该类方程的数值方法研究成果较少.针对带Poisson测度的随机微分方程,在非Lipschitz条件下证明了Euler方法的依概率收敛性,并给出相应的数值算例支持主要结论.Euler method was introduced to stochastic differential equations（SDEs） with Poisson measure under the Non-Lipschitz conditions which cover more classes of such equations than classical conditions.Few results about numerical methods were presented to such equations in current literature.Proved the convergence of the Euler method in probability under the Non-Lipschitz conditions,and gave an numerical example was given to show the main result.

关 键 词：随机微分方程 POISSON 测度 非Lipschitz 条件 EULER方法 依概率收敛 

分 类 号：O211.63[理学—概率论与数理统计]