The Weak Euler Scheme for StochasticDifferential Delay Equations
The Weak Euler Scheme for StochasticDifferential Delay Equations
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发表时间：
2006-01
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通讯作者：
E. Buckwar;R. Kuske;S. Mohammed;T. Shardlow
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作者：
E. Buckwar;R. Kuske;S. Mohammed;T. Shardlow
研究了由多维布朗运动驱动的非线性随机时滞微分方程（SDDEs）的弱数值欧拉格式。弱欧拉格式的收敛阶为1，如在随机常微分方程（SODEs）的情况下（即，无延迟）。该结果适用于漂移项和扩散项具有多个有限固定延迟的SDDEs。虽然设置是不可预测的，但我们的方法使用了Malliavin演算和Nualart和Pardoux的预测随机分析技术。
We develop a weak numerical Euler scheme for non-linear stochastic delay differential equations (SDDEs) driven by multidimensional Brownian motion. The weak Euler scheme has order of convergence 1, as in the case of stochastic ordinary differential equations (SODEs) (i.e., without delay).The result holds for SDDEs with multiple finite fixed delays in the drift and diffusion terms. Although the set-up is non-anticipating, our approach uses the Malliavin calculus and the anticipating stochastic analysis techniques of Nualart and Pardoux.