Covariance of stochastic integrals with respect to fractional Brownian motion

Yohaï Maayan; Eddy Mayer-Wolf

doi:https://doi.org/10.1016/j.spa.2017.08.006

Covariance of stochastic integrals with respect to fractional Brownian motion

Yohaï Maayan, Eddy Mayer-Wolf

Mathematics

Technion - Israel Institute of Technology

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

Abstract

We find an explicit expression for the cross-covariance between stochastic integral processes with respect to a d-dimensional fractional Brownian motion (fBm) B_t with Hurst parameter H>[Formula presented], where the integrands are vector fields applied to B_t. It provides, for example, a direct alternative proof of Y. Hu and D. Nualart's result that the stochastic integral component in the fractional Bessel process decomposition is not itself a fractional Brownian motion.

Original language	English
Pages (from-to)	1635-1651
Number of pages	17
Journal	Stochastic Processes and their Applications
Volume	128
Issue number	5
DOIs	https://doi.org/10.1016/j.spa.2017.08.006
State	Published - May 2018

Keywords

Divergence integral
Fractional Bessel process
Fractional Brownian motion
Stochastic integral

All Science Journal Classification (ASJC) codes

Applied Mathematics
Statistics and Probability
Modelling and Simulation

Access to Document

https://doi.org/10.1016/j.spa.2017.08.006

Cite this

@article{bf8e32c5fa0a41b080e95971cc6e28e8,

title = "Covariance of stochastic integrals with respect to fractional Brownian motion",

abstract = "We find an explicit expression for the cross-covariance between stochastic integral processes with respect to a d-dimensional fractional Brownian motion (fBm) Bt with Hurst parameter H>[Formula presented], where the integrands are vector fields applied to Bt. It provides, for example, a direct alternative proof of Y. Hu and D. Nualart's result that the stochastic integral component in the fractional Bessel process decomposition is not itself a fractional Brownian motion.",

keywords = "Divergence integral, Fractional Bessel process, Fractional Brownian motion, Stochastic integral",

author = "Yoha{\"i} Maayan and Eddy Mayer-Wolf",

note = "Publisher Copyright: {\textcopyright} 2017 Elsevier B.V.",

year = "2018",

month = may,

doi = "https://doi.org/10.1016/j.spa.2017.08.006",

language = "الإنجليزيّة",

volume = "128",

pages = "1635--1651",

journal = "Stochastic Processes and their Applications",

issn = "0304-4149",

publisher = "Elsevier B.V.",

number = "5",

}

TY - JOUR

T1 - Covariance of stochastic integrals with respect to fractional Brownian motion

AU - Maayan, Yohaï

AU - Mayer-Wolf, Eddy

PY - 2018/5

Y1 - 2018/5

N2 - We find an explicit expression for the cross-covariance between stochastic integral processes with respect to a d-dimensional fractional Brownian motion (fBm) Bt with Hurst parameter H>[Formula presented], where the integrands are vector fields applied to Bt. It provides, for example, a direct alternative proof of Y. Hu and D. Nualart's result that the stochastic integral component in the fractional Bessel process decomposition is not itself a fractional Brownian motion.

AB - We find an explicit expression for the cross-covariance between stochastic integral processes with respect to a d-dimensional fractional Brownian motion (fBm) Bt with Hurst parameter H>[Formula presented], where the integrands are vector fields applied to Bt. It provides, for example, a direct alternative proof of Y. Hu and D. Nualart's result that the stochastic integral component in the fractional Bessel process decomposition is not itself a fractional Brownian motion.

KW - Divergence integral

KW - Fractional Bessel process

KW - Fractional Brownian motion

KW - Stochastic integral

UR - http://www.scopus.com/inward/record.url?scp=85028581553&partnerID=8YFLogxK

U2 - https://doi.org/10.1016/j.spa.2017.08.006

DO - https://doi.org/10.1016/j.spa.2017.08.006

M3 - مقالة

SN - 0304-4149

VL - 128

SP - 1635

EP - 1651

JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

IS - 5

ER -

Covariance of stochastic integrals with respect to fractional Brownian motion

Abstract

Keywords

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this