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2010 Weak approximation of fractional SDEs: the Donsker setting
Xavier Bardina, Carles Rovira, Samy Tindel
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Electron. Commun. Probab. 15: 314-329 (2010). DOI: 10.1214/ECP.v15-1561


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 $H\in(1/3,1/2)$, initiated in a paper of Bardina et al. . 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. Carles Rovira. Samy Tindel. "Weak approximation of fractional SDEs: the Donsker setting." Electron. Commun. Probab. 15 314 - 329, 2010.


Accepted: 23 July 2010; Published: 2010
First available in Project Euclid: 6 June 2016

zbMATH: 1225.60091
MathSciNet: MR2670198
Digital Object Identifier: 10.1214/ECP.v15-1561

Primary: 60H10
Secondary: 60H05

Keywords: fractional Brownian motion , Kac-Stroock type approximation , Rough paths , weak approximation

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