Optimal approximation of SDE's with additive fractional noise
Optimal approximation of SDE's with additive fractional noise
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DOI：
10.1016/j.jco.2006.02.001
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发表时间：
2006-08
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影响因子：
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通讯作者：
A. Neuenkirch
中科院分区：
文献类型：
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作者：
A. Neuenkirch
We study pathwise approximation of scalar stochastic differential equations with additive fractional Brownian noise of Hurst parameter H>12, considering the mean square L2-error criterion. By means of the Malliavin calculus we derive the exact rate of convergence of the Euler scheme, also for non-equidistant discretizations. Moreover, we establish a sharp lower error bound that holds for arbitrary methods, which use a fixed number of bounded linear functionals of the driving fractional Brownian motion. The Euler scheme based on a discretization, which reflects the local smoothness properties of the equation, matches this lower error bound up to the factor 1.39.
