Optimal pointwise approximation of stochastic differential equations driven by fractional Brownian motion

Neuenkirch, Andreas

URL: https://arxiv.org/abs/0706.2636
Document Type: Working paper
Year of publication: 2007
Place of publication: Ithaca, NY
Publishing house: Cornell University
Publication language: English
Institution: School of Business Informatics and Mathematics > Wirtschaftsmathematik II: Stochastische Numerik (Neuenkirch 2013-)
Subject: 510 Mathematics
Abstract: We study the approximation of stochastic differential equations driven by a fractional Brownian motion with Hurst parameter H>1/2. For the mean-square error at a single point we derive the optimal rate of convergence that can be achieved by any approximation method using 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−1/2, where n 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.

Dieser Datensatz wurde nicht während einer Tätigkeit an der Universität Mannheim veröffentlicht, dies ist eine Externe Publikation.

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