A weak trapezoidal method for a class of stochastic differential equations
A weak trapezoidal method for a class of stochastic differential equations
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DOI：
10.4310/cms.2011.v9.n1.a15
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发表时间：
2009-06
期刊：
影响因子：
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通讯作者：
David F. Anderson;Jonathan C. Mattingly
中科院分区：
文献类型：
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作者：
David F. Anderson;Jonathan C. Mattingly
给出了一类由布朗运动驱动的随机微分方程解的数值逼近方法，该方程在固定方向上产生随机变差。这类方程在人口过程和化学反应动力学的研究中自然出现。我们表明，该方法构造的路径是二阶准确的弱意义。该方法比许多二阶方法简单，因为它既不需要迭代Ito积分的建设，也不需要任何衍生物的评估。该方法包括两个步骤。在第一个显式欧拉步骤是用来采取一个分数的步骤。然后将该分数点与初始点组合以获得更高阶的梯形近似。更高阶的准确度源于以下事实：基础SDE的漂移和二次变差都接近二阶。
We present a numerical method for the approximation of solutions for the class of stochastic differential equations driven by Brownian motions which induce stochastic variation in fixed directions. This class of equations arises naturally in the study of population processes and chemical reaction kinetics. We show that the method constructs paths that are second order accurate in the weak sense. The method is simpler than many second order methods in that it neither requires the construction of iterated Ito integrals nor the evaluation of any derivatives. The method consists of two steps. In the first an explicit Euler step is used to take a fractional step. This fractional point is then combined with the initial point to obtain a higher order, trapezoidal like, approximation. The higher order of accuracy stems from the fact that both the drift and the quadratic variation of the underlying SDE are approximated to second order.