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Weak approximation of fractional SDEs: the Donsker setting


 
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1. Title Title of document Weak approximation of fractional SDEs: the Donsker setting
 
2. Creator Author's name, affiliation, country Xavier Bardina; Universitat Autònoma de Barcelona
 
2. Creator Author's name, affiliation, country Carles Rovira; Universitat de Barcelona
 
2. Creator Author's name, affiliation, country Samy Tindel; Institut Elie Cartan Nancy
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Weak approximation, Kac-Stroock type approximation, fractional Brownian motion, rough paths
 
3. Subject Subject classification 60H10, 60H05
 
4. Description 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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7. Date (YYYY-MM-DD) 2010-07-23
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ecp.ejpecp.org/article/view/1561
 
10. Identifier Digital Object Identifier 10.1214/ECP.v15-1561
 
11. Source Journal/conference title; vol., no. (year) Electronic Communications in Probability; Vol 15
 
12. Language English=en
 
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