Weak approximation of fractional SDES: The Donsker setting

Xavier Bardina; Samy Tindel; Carles Rovira

Weak approximation of fractional SDES: The Donsker setting

Probability 2009-07-20 v1

Authors: Xavier Bardina , Samy Tindel , Carles Rovira

Abstract

In this note, we take up the study of weak convergence for stochastic differential equations driven by a (Liouville) fractional Brownian motion $B$ with Hurst parameter $H\in(1/3,1/2)$ . In the current paper, we approximate the $d$ -dimensional fBm by the convolution of a rescaled random walk with Liouville's kernel. We then show that the corresponding differential equation converges in law to a fractional SDE driven by $B$ .

Keywords

fractional Brownian motion weak convergence stochastic differential equations Donsker approximation Liouville kernel Hurst parameter

Cite

@article{arxiv.0907.3030,
  title  = {Weak approximation of fractional SDES: The Donsker setting},
  author = {Xavier Bardina and Samy Tindel and Carles Rovira},
  journal= {arXiv preprint arXiv:0907.3030},
  year   = {2009}
}

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