Stochastic Analysis of the Fractional Brownian Motion

L. Decreusefond; A. S. Üstünel

doi:10.1023/A:1008634027843

Stochastic Analysis of the Fractional Brownian Motion

L. Decreusefond
, A. S. Üstünel

Telecom Paris

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

Abstract

Since the fractional Brownian motion is not a semi-martingale, the usual Ito calculus cannot be used to define a full stochastic calculus. However, in this work, we obtain the Itô formula, the Itô-Clark representation formula and the Girsanov theorem for the functionals of a fractional Brownian motion using the stochastic calculus of variations.

Original language	English
Pages (from-to)	177-214
Number of pages	38
Journal	Potential Analysis
Volume	10
Issue number	2
DOIs	https://doi.org/10.1023/A:1008634027843
Publication status	Published - 1 Jan 1999

Keywords

Fractional Brownian motion
Girsanov formula
Itô formula
Stochastic calculus of variations

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title = "Stochastic Analysis of the Fractional Brownian Motion",

abstract = "Since the fractional Brownian motion is not a semi-martingale, the usual Ito calculus cannot be used to define a full stochastic calculus. However, in this work, we obtain the It{\^o} formula, the It{\^o}-Clark representation formula and the Girsanov theorem for the functionals of a fractional Brownian motion using the stochastic calculus of variations.",

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year = "1999",

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AU - Decreusefond, L.

AU - Üstünel, A. S.

PY - 1999/1/1

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N2 - Since the fractional Brownian motion is not a semi-martingale, the usual Ito calculus cannot be used to define a full stochastic calculus. However, in this work, we obtain the Itô formula, the Itô-Clark representation formula and the Girsanov theorem for the functionals of a fractional Brownian motion using the stochastic calculus of variations.

AB - Since the fractional Brownian motion is not a semi-martingale, the usual Ito calculus cannot be used to define a full stochastic calculus. However, in this work, we obtain the Itô formula, the Itô-Clark representation formula and the Girsanov theorem for the functionals of a fractional Brownian motion using the stochastic calculus of variations.

KW - Fractional Brownian motion

KW - Girsanov formula

KW - Itô formula

KW - Stochastic calculus of variations

UR - https://www.scopus.com/pages/publications/0042637937

U2 - 10.1023/A:1008634027843

DO - 10.1023/A:1008634027843

M3 - Article

AN - SCOPUS:0042637937

SN - 0926-2601

VL - 10

SP - 177

EP - 214

JO - Potential Analysis

JF - Potential Analysis

IS - 2

ER -

Stochastic Analysis of the Fractional Brownian Motion

Abstract

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