Article ID Journal Published Year Pages File Type
1156265 Stochastic Processes and their Applications 2008 40 Pages PDF
Abstract

We study the approximation of stochastic differential equations driven by a fractional Brownian motion with Hurst parameter H>1/2H>1/2. For the mean-square error at a single point we derive the optimal rate of convergence that can be achieved by arbitrary approximation methods that are based on an equidistant discretization of the driving fractional Brownian motion. We find that there are mainly two cases: either the solution can be approximated perfectly or the best possible rate of convergence is n−H−1/2n−H−1/2, where nn denotes the number of evaluations of the fractional Brownian motion. In addition, we present an implementable approximation scheme that obtains the optimal rate of convergence in the latter case.

Related Topics
Physical Sciences and Engineering Mathematics Mathematics (General)
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