Continuity with respect to the Hurst parameter of the laws of the multiple fractional integrals

Maria Jolis; Noèlia Viles

doi:https://doi.org/10.1016/j.spa.2006.12.005

Continuity with respect to the Hurst parameter of the laws of the multiple fractional integrals

Maria Jolis, Noèlia Viles

Department of Mathematics

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

5 Citations (Scopus)

Abstract

We prove the weak convergence in C ([0, T]) of the laws of the Itô and Stratonovich multiple integrals of some classes of deterministic functions with respect to the fractional Brownian motion, BH, with Hurst parameter H > 1 / 2, to the law of the corresponding multiple integral with respect to BH0, when H tends to H0 ∈ [1 / 2, 1). © 2007 Elsevier Ltd. All rights reserved.

Original language	English
Pages (from-to)	1189-1207
Journal	Stochastic Processes and their Applications
Volume	117
DOIs	https://doi.org/10.1016/j.spa.2006.12.005
Publication status	Published - 1 Sept 2007

Keywords

Convergence in law
Fractional Brownian motion
Itô-type multiple integral
Stratonovich-type multiple integral

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https://doi.org/10.1016/j.spa.2006.12.005

Cite this

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abstract = "We prove the weak convergence in C ([0, T]) of the laws of the It{\^o} and Stratonovich multiple integrals of some classes of deterministic functions with respect to the fractional Brownian motion, BH, with Hurst parameter H > 1 / 2, to the law of the corresponding multiple integral with respect to BH0, when H tends to H0 ∈ [1 / 2, 1). {\textcopyright} 2007 Elsevier Ltd. All rights reserved.",

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author = "Maria Jolis and No{\`e}lia Viles",

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T1 - Continuity with respect to the Hurst parameter of the laws of the multiple fractional integrals

AU - Jolis, Maria

AU - Viles, Noèlia

PY - 2007/9/1

Y1 - 2007/9/1

N2 - We prove the weak convergence in C ([0, T]) of the laws of the Itô and Stratonovich multiple integrals of some classes of deterministic functions with respect to the fractional Brownian motion, BH, with Hurst parameter H > 1 / 2, to the law of the corresponding multiple integral with respect to BH0, when H tends to H0 ∈ [1 / 2, 1). © 2007 Elsevier Ltd. All rights reserved.

AB - We prove the weak convergence in C ([0, T]) of the laws of the Itô and Stratonovich multiple integrals of some classes of deterministic functions with respect to the fractional Brownian motion, BH, with Hurst parameter H > 1 / 2, to the law of the corresponding multiple integral with respect to BH0, when H tends to H0 ∈ [1 / 2, 1). © 2007 Elsevier Ltd. All rights reserved.

KW - Convergence in law

KW - Fractional Brownian motion

KW - Itô-type multiple integral

KW - Stratonovich-type multiple integral

U2 - https://doi.org/10.1016/j.spa.2006.12.005

DO - https://doi.org/10.1016/j.spa.2006.12.005

M3 - Article

SN - 0304-4149

VL - 117

SP - 1189

EP - 1207

JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

ER -

Continuity with respect to the Hurst parameter of the laws of the multiple fractional integrals

Abstract

Keywords

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