Asymptotic behavior of weighted quadratic variation of bi-fractional Brownian motion

Rachid Belfadli[1]

  • [1] Department of Mathematics Cadi Ayyad University Semlalia Faculty of Sciences 2390 Marrakesh Morocco

Annales mathématiques Blaise Pascal (2010)

  • Volume: 17, Issue: 1, page 165-181
  • ISSN: 1259-1734

Abstract

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We prove, by means of Malliavin calculus, the convergence in L 2 of some properly renormalized weighted quadratic variations of bi-fractional Brownian motion (biFBM) with parameters H and K , when H < 1 / 4 and K ∈ ( 0 , 1 ] .

How to cite

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Belfadli, Rachid. "Asymptotic behavior of weighted quadratic variation of bi-fractional Brownian motion." Annales mathématiques Blaise Pascal 17.1 (2010): 165-181. <http://eudml.org/doc/116346>.

@article{Belfadli2010,
abstract = {We prove, by means of Malliavin calculus, the convergence in $L^\{2\}$ of some properly renormalized weighted quadratic variations of bi-fractional Brownian motion (biFBM) with parameters $H$ and $K$, when $H&lt;1/4$ and $K\in (0,1]$.},
affiliation = {Department of Mathematics Cadi Ayyad University Semlalia Faculty of Sciences 2390 Marrakesh Morocco},
author = {Belfadli, Rachid},
journal = {Annales mathématiques Blaise Pascal},
keywords = {Bi-fractional Brownian motion; Weighted quadratic variations; Malliavan calculus; bi-fractional Brownian motion; weighted quadratic variations; Malliavin calculus},
language = {eng},
month = {1},
number = {1},
pages = {165-181},
publisher = {Annales mathématiques Blaise Pascal},
title = {Asymptotic behavior of weighted quadratic variation of bi-fractional Brownian motion},
url = {http://eudml.org/doc/116346},
volume = {17},
year = {2010},
}

TY - JOUR
AU - Belfadli, Rachid
TI - Asymptotic behavior of weighted quadratic variation of bi-fractional Brownian motion
JO - Annales mathématiques Blaise Pascal
DA - 2010/1//
PB - Annales mathématiques Blaise Pascal
VL - 17
IS - 1
SP - 165
EP - 181
AB - We prove, by means of Malliavin calculus, the convergence in $L^{2}$ of some properly renormalized weighted quadratic variations of bi-fractional Brownian motion (biFBM) with parameters $H$ and $K$, when $H&lt;1/4$ and $K\in (0,1]$.
LA - eng
KW - Bi-fractional Brownian motion; Weighted quadratic variations; Malliavan calculus; bi-fractional Brownian motion; weighted quadratic variations; Malliavin calculus
UR - http://eudml.org/doc/116346
ER -

References

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  8. D. Nualart, The Malliavin calculus and related topics, (2006), Springer Verlag, 2 nd edition, Berlin Zbl1099.60003MR2200233
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  11. C. A. Tudor, Y. Xiao, Sample Path Properties of Bifractional Brownian Motion, Bernoulli 13 (4) (2007), 1023-1052 Zbl1132.60034MR2364225

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