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Weak and strong discrete-time approximation of fractional SDEs∗

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Abstract

We study discrete-time approximations of Gaussian processes of the form Z H = ∫ .0 σ s dB H s and of SDEs driven by Z H, where σ is a deterministic (possibly, discontinuous) function, and B H is a fractional Brownian motion with Hurst index H >1/2. The classical approximation methods used previously in the case σ ≡ 1 are refined. Our schemes are based on an integral representation of B H given by Decreusefond and Ustunel. Applications to approximation of option prices in fractional models are given.

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Authors and Affiliations

  1. Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, Chopina str. 12/18, 87-100, Toruń, Poland

    Adrian Falkowski, Leszek Słomiński & Bartosz Ziemkiewicz

Authors
  1. Adrian Falkowski
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  2. Leszek Słomiński
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  3. Bartosz Ziemkiewicz
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Correspondence to Leszek Słomiński.

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*Research supported by Polish National Science Centre (grant No. 2012/07/B/ST1/03508).

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Falkowski, A., Słomiński, L. & Ziemkiewicz, B. Weak and strong discrete-time approximation of fractional SDEs∗ . Lith Math J 54, 409–428 (2014). https://doi.org/10.1007/s10986-014-9253-9

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  • DOI: https://doi.org/10.1007/s10986-014-9253-9

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