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arXiv · 0907.3030

Weak approximation of fractional SDES: The Donsker setting

Xavier Bardina·Samy Tindel·Carles Rovira
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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 $B$.

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Xavier Bardina, Samy Tindel, Carles Rovira. 2009-07-17. Weak approximation of fractional SDES: The Donsker setting. https://arxiv.org/abs/0907.3030

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