线性随机时滞微分方程裂步Milstein方法的收敛性
선성수궤시체미분방정렬보Milstein방법적수렴성
Convergence of split-step Milstein method for linear stochastic delay differential equations
  • 万方数据
    应用数学与计算数学学报 응용수학여계산수학학보
    COMMUNICATION ON APPLIED MATHEMATICS AND COMPUTATION
    2012年 4期 456-464 ,共9页

    郭谦%解雯雯%陶雪银%朱颖

    곽겸%해문문%도설은%주영

    随机时滞微分方程%Milstein格式%分裂步长%强收敛 隨機時滯微分方程%Milstein格式%分裂步長%彊收斂
    수궤시체미분방정%Milstein격식%분렬보장%강수렴
    stochastic delay differential equation%Milstein scheme%split-step%strong convergence
    给出一个新的求解线性随机时滞微分方程的显式分裂步长Milstein格式. 运用Ito-Taylor展开式证明该格式相对于已有的求解随机时滞微分方程的分裂步长方法而言具有更好的收敛性. 数值实验验证了理论分析的正确性.
    급출일개신적구해선성수궤시체미분방정적현식분렬보장Milstein격식. 운용Ito-Taylor전개식증명해격식상대우이유적구해수궤시체미분방정적분렬보장방법이언구유경호적수렴성. 수치실험험증료이론분석적정학성.
    A new explicit split-step Milstein method for solving linear Ito stochastic differential equations (SDEs) with a constant time delay is introduced. The Ito-Taylor expansion is employed to prove the strong convergence, which inproves the convergence results of known split-step methods for stochastic delay differential equations (SDDEs). Numerical experiments confirm the theoretical results.
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