Numerical Integration of Stochastic Differential Equations with Nonglobally Lipschitz Coefficients
Numerical Integration of Stochastic Differential Equations with Nonglobally Lipschitz Coefficients
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DOI：
10.1137/040612026
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发表时间：
2005-03
期刊：
影响因子：
--
通讯作者：
G. Milstein;M. Tretyakov
中科院分区：
文献类型：
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作者：
G. Milstein;M. Tretyakov
我们提出了一个新的概念，使我们能够适用于任何数值方法的弱近似的一类非常广泛的随机微分方程（SDES）与nonglobally Lipschitz系数。根据这个概念，我们放弃了留下足够大的球的近似轨迹。我们证明，任何弱阶p方法的精度都可以通过$\varepsilon +O（h^{p}）估计，$其中$\varepsilon $可以随着球体半径的增加而任意小。所得结果得到了数值实验的支持。
We propose a new concept which allows us to apply any numerical method of weak approximation to a very broad class of stochastic differential equations (SDEs) with nonglobally Lipschitz coefficients. Following this concept, we discard the approximate trajectories which leave a sufficiently large sphere. We prove that accuracy of any method of weak order p is estimated by $\varepsilon +O(h^{p}),$ where $\varepsilon $ can be made arbitrarily small with increasing radius of the sphere. The results obtained are supported by numerical experiments.