随机微分方程的连续弱逼近
Continuous Weak Approximation for Stochastic Differential Equations
AI总结：
针对随机微分方程解的连续弱逼近，推广了Milstein定理，推导了一类连续随机Runge-Kutta方法的二阶条件，并给出了适用于多维Wiener过程的Itô随机微分方程的最优连续格式系数。
摘要：
证明了一个关于一般单步方法对随机微分方程解的连续弱逼近的收敛定理，这是对Milstein定理的推广。作为应用，推导了一类连续随机Runge-Kutta方法的统一二阶条件，其中包含Platen提出的二阶随机Runge-Kutta格式的连续延拓。此外，给出了一些适用于关于多维Wiener过程的Itô随机微分方程的最优连续格式的系数。
英文摘要：
A convergence theorem for the continuous weak approximation of the solution of stochastic differential equations by general one step methods is proved, which is an extension of a theorem due to Milstein. As an application, uniform second order conditions for a class of continuous stochastic Runge-Kutta methods containing the continuous extension of the second order stochastic Runge-Kutta scheme due to Platen are derived. Further, some coefficients for optimal continuous schemes applicable to Itô stochastic differential equations with respect to a multi-dimensional Wiener process are presented.
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