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首页> 外文期刊>Stochastic Processes and Their Applications: An Official Journal of the Bernoulli Society for Mathematical Statistics and Probability >Weak consistency of the Euler method for numerically solving stochastic differential equations with discontinuous coefficients
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Weak consistency of the Euler method for numerically solving stochastic differential equations with discontinuous coefficients

机译：求解具有不连续系数的随机微分方程的Euler方法的弱一致性

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摘要

We prove that, under appropriate conditions, the sequence of approximate solutions constructed according to the Euler scheme converges weakly to the (unique) solution of a stochastic differential equation with discontinuous coefficients. We also obtain a sufficient condition for the existence of a solution to a stochastic differential equation with discontinuous coefficients. These results are then applied to justify the technique of simulating continuous-time threshold autoregressive moving-average processes via the Euler scheme. (C) 1998 Elsevier Science B.V. All rights reserved. [References: 20]
机译：我们证明，在适当的条件下，根据欧拉方案构造的近似解的序列弱收敛到具有不连续系数的随机微分方程的（唯一）解。我们还获得了具有不连续系数的随机微分方程解的存在性的充分条件。然后将这些结果用于证明通过Euler方案模拟连续时间阈值自回归移动平均过程的技术的合理性。 （C）1998 Elsevier Science B.V.保留所有权利。 [参考：20]

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