Electronic Communications in Probability

Weak approximation of fractional SDEs: the Donsker setting

Xavier Bardina, Carles Rovira, and Samy Tindel

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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 $B$.

Article information

Electron. Commun. Probab., Volume 15 (2010), paper no. 30, 314-329.

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60H10: Stochastic ordinary differential equations [See also 34F05]
Secondary: 60H05: Stochastic integrals

Weak approximation Kac-Stroock type approximation fractional Brownian motion rough paths

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Bardina, Xavier; Rovira, Carles; Tindel, Samy. Weak approximation of fractional SDEs: the Donsker setting. Electron. Commun. Probab. 15 (2010), paper no. 30, 314--329. doi:10.1214/ECP.v15-1561. https://projecteuclid.org/euclid.ecp/1465243973

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