Weak approximation of fractional sdes: The donsker setting

Xavier Bardina, Carles Rovira, Samy Tindel

Research output: Contribution to journalArticleResearchpeer-review

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 [3]. 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. © 2010 Applied Probability Trust.
Original languageEnglish
Pages (from-to)314-329
JournalElectronic Communications in Probability
Volume15
DOIs
Publication statusPublished - 1 Jan 2010

Keywords

  • Fractional Brownian motion
  • Kac-Stroock type approximation
  • Rough paths
  • Weak approximation

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