MR2565851). 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 $B$.">
Weak approximation of fractional SDEs: the Donsker setting
Xavier Bardina, Universitat Autònoma de Barcelona
Carles Rovira, Universitat de Barcelona
Samy Tindel, Institut Elie Cartan Nancy
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 $H∈ (1/3,1/2)$,
initiated in a paper of Bardina et al. (2010, MR2565851). 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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