求解带跳随机微分方程的一类全隐式方法

Fully implicit methods for solving stochastic jump-diffusion equations

为更好地解决求解带跳的随机微分方程问题,将目前有关求解方程的隐式方法推广到跳跃项的隐式化,进而构造一类新的全隐式方法:补偿θ-Balanced数值方法.首先证明此数值方法是1.5阶均值相容,1阶均方相容;然后证明由此方法所得的数值解是收敛到解析解的,且收敛阶为0.5.最后,通过数值算例说明所构造的数值方法的有效性.

To improve the performance of numerical methods for solving stochastic differential equations with jumps,the implicit method for solving equations is developed into considering the implicitness in jump term,and a new class of fully implicit methods：The compensatedθ-balanced numerical methods is prosed.Firstly,it is proved that the numerical method is consistent with order 1.5 in the mean and with order 1.0 in the mean square.Then,it is also proved that the proposed numerical solutions converge to the analytical solutions with rate of 0.5.Finally,some numerical experiments are given to evaluate the performance of the proposed numerical methods.