Weak approximation of fractional sdes: The donsker setting

Xavier Bardina; Carles Rovira; Samy Tindel

doi:10.1214/ECP.v15-1561

Weak approximation of fractional sdes: The donsker setting

Xavier Bardina, Carles Rovira, Samy Tindel

Research output: Contribution to journal › Article › Research › peer-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 language	English
Pages (from-to)	314-329
Journal	Electronic Communications in Probability
Volume	15
DOIs	https://doi.org/10.1214/ECP.v15-1561
Publication status	Published - 1 Jan 2010

Keywords

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

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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 {\textquoteright}s kernel. We then show that the corresponding differential equation converges in law to a fractional SDE driven by B. {\textcopyright} 2010 Applied Probability Trust.",

keywords = "Fractional Brownian motion, Kac-Stroock type approximation, Rough paths, Weak approximation",

author = "Xavier Bardina and Carles Rovira and Samy Tindel",

year = "2010",

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doi = "10.1214/ECP.v15-1561",

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T1 - Weak approximation of fractional sdes: The donsker setting

AU - Bardina, Xavier

AU - Rovira, Carles

AU - Tindel, Samy

PY - 2010/1/1

Y1 - 2010/1/1

N2 - 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.

AB - 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.

KW - Fractional Brownian motion

KW - Kac-Stroock type approximation

KW - Rough paths

KW - Weak approximation

UR - https://www.scopus.com/pages/publications/77955465491

U2 - 10.1214/ECP.v15-1561

DO - 10.1214/ECP.v15-1561

M3 - Article

SN - 1083-589X

VL - 15

SP - 314

EP - 329

JO - Electronic Communications in Probability

JF - Electronic Communications in Probability

ER -

Weak approximation of fractional sdes: The donsker setting

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Keywords

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