Weak approximation of fractional SDES: The Donsker setting

Details Weak approximation of fractional SDES: The Donsker setting Weak approximation of fractional SDES: The Donsker setting

2009-07-17

arxiv.org/abs/0907.3030v1

Mathematics

Probability

Scientific paper

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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