粗糙路径驱动的微分方程:一种离散逼近方法

Applied mathematics research express : AMRX Pub Date : 2007-10-03 DOI:10.1093/AMRX/ABM009

A. Davie

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引用次数: 212

摘要

驱动路径x(t)是不可微的，最近由Lyons提出。我开发了一种替代方法，使用(修改的)欧拉近似，并研究其对布朗运动驱动的随机微分方程的适用性。我还提供了一些其他的例子来说明主要的结果是相当清晰的。

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Differential Equations Driven by Rough Paths: An Approach via Discrete Approximation

driving path x(t) is nondifferentiable, has recently been developed by Lyons. I develop an alternative approach to this theory, using (modified) Euler approximations, and investigate its applicability to stochastic differential equations driven by Brownian motion. I also give some other examples showing that the main results are reasonably sharp.

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Applied mathematics research express : AMRX

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