Weak approximation of a fractional SDE

X. Bardina; I. Nourdin; C. Rovira; S. Tindel

doi:https://doi.org/10.1016/j.spa.2009.10.008

Weak approximation of a fractional SDE

X. Bardina, I. Nourdin, C. Rovira, S. Tindel

Research output: Contribution to journal › Article › Research › peer-review

6 Citations (Scopus)

Abstract

In this note, a diffusion approximation result is shown for stochastic differential equations driven by a (Liouville) fractional Brownian motion B with Hurst parameter H ∈ (1 / 3, 1 / 2). More precisely, we resort to the Kac-Stroock type approximation using a Poisson process studied in Bardina et al. (2003) [4] and Delgado and Jolis (2000) [9], and our method of proof relies on the algebraic integration theory introduced by Gubinelli in Gubinelli (2004) [14]. © 2009 Elsevier B.V. All rights reserved.

Original language	English
Pages (from-to)	39-65
Journal	Stochastic Processes and their Applications
Volume	120
DOIs	https://doi.org/10.1016/j.spa.2009.10.008
Publication status	Published - 1 Jan 2010

Keywords

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

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https://doi.org/10.1016/j.spa.2009.10.008

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title = "Weak approximation of a fractional SDE",

abstract = "In this note, a diffusion approximation result is shown for stochastic differential equations driven by a (Liouville) fractional Brownian motion B with Hurst parameter H ∈ (1 / 3, 1 / 2). More precisely, we resort to the Kac-Stroock type approximation using a Poisson process studied in Bardina et al. (2003) [4] and Delgado and Jolis (2000) [9], and our method of proof relies on the algebraic integration theory introduced by Gubinelli in Gubinelli (2004) [14]. {\textcopyright} 2009 Elsevier B.V. All rights reserved.",

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

author = "X. Bardina and I. Nourdin and C. Rovira and S. Tindel",

year = "2010",

month = jan,

day = "1",

doi = "https://doi.org/10.1016/j.spa.2009.10.008",

language = "English",

volume = "120",

pages = "39--65",

journal = "Stochastic Processes and their Applications",

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TY - JOUR

T1 - Weak approximation of a fractional SDE

AU - Bardina, X.

AU - Nourdin, I.

AU - Rovira, C.

AU - Tindel, S.

PY - 2010/1/1

Y1 - 2010/1/1

N2 - In this note, a diffusion approximation result is shown for stochastic differential equations driven by a (Liouville) fractional Brownian motion B with Hurst parameter H ∈ (1 / 3, 1 / 2). More precisely, we resort to the Kac-Stroock type approximation using a Poisson process studied in Bardina et al. (2003) [4] and Delgado and Jolis (2000) [9], and our method of proof relies on the algebraic integration theory introduced by Gubinelli in Gubinelli (2004) [14]. © 2009 Elsevier B.V. All rights reserved.

AB - In this note, a diffusion approximation result is shown for stochastic differential equations driven by a (Liouville) fractional Brownian motion B with Hurst parameter H ∈ (1 / 3, 1 / 2). More precisely, we resort to the Kac-Stroock type approximation using a Poisson process studied in Bardina et al. (2003) [4] and Delgado and Jolis (2000) [9], and our method of proof relies on the algebraic integration theory introduced by Gubinelli in Gubinelli (2004) [14]. © 2009 Elsevier B.V. All rights reserved.

KW - Fractional Brownian motion

KW - Kac-Stroock type approximation

KW - Rough paths

KW - Weak approximation

U2 - https://doi.org/10.1016/j.spa.2009.10.008

DO - https://doi.org/10.1016/j.spa.2009.10.008

M3 - Article

SN - 0304-4149

VL - 120

SP - 39

EP - 65

JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

ER -

Weak approximation of a fractional SDE

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Keywords

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