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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 Electronic Communications in Probability > Vol. 15(2010) > Paper 30 open journal systems 


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 $B$.


Full text: PDF

Pages: 314-329

Published on: July 23, 2010


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