胡军浩,方明,高帅斌.混杂随机泛函微分方程修正截断EM算法的强收敛率[J].中南民族大学学报自然科学版,2019,(2):291-297
混杂随机泛函微分方程修正截断EM算法的强收敛率
Strong convergence rate of modified truncated EM algorithm of hybrid stochastic functional differential equations
  
DOI:10.12130/znmdzk.20190225
中文关键词: 随机泛函微分方程  混杂系统  截断EM算法  强收敛率
英文关键词: stochastic functional differential equations  hybrid systems  truncated EM algorithm  strong convergence rate
基金项目:国家自然科学基金资助项目(61876192)
作者单位
胡军浩,方明,高帅斌 中南民族大学 数学与统计学学院武汉430074 
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中文摘要:
      对于非线性混杂随机泛函微分方程的数值解,提出一种新的在空间和时间上都截断的EM数值算法. 该算法在空间上截断主要针对的是非线性系数,在时间上截断主要改善泛函方程数值算法的复杂度. 根据此算法,得出非线性混杂随机泛函微分方程数值解的强收敛率,理论结果表明:强收敛率和Markovian切换有关. 最后,给出一个例子说明算法的有效性.
英文摘要:
      In this paper, the new modified truncated EM numerical algorithm of nonlinear hybrid stochastic functional differential equations is proposed. The nonlinear coefficients of these equations are truncated in space, and, the complexity of the algorithm is improved by truncated in time. According to the new algorithm, the strong convergence rate of the numerical solutions of these equations is obtained. The strong convergence rate depends on Markovian switching. Finally, an example is provided to illustrate the effectiveness of the algorithm.
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