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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


An Itô formula for a fractional Brownian sheet with arbitrary Hurst parameters

Authors: Yoon Tae Kim and Jong Woo Jeon
Journal: Proc. Amer. Math. Soc. 134 (2006), 3677-3683
MSC (2000): Primary 60H07; Secondary 60G18
Published electronically: June 9, 2006
MathSciNet review: 2240682
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Abstract | References | Similar Articles | Additional Information

Abstract: By using the white noise theory for a fractional Brownian sheet, we derive an Itô formula for the fractional Brownian sheet with arbitrary Hurst parameters $ H_{1}, H_{2}\in (0,1)$.

References [Enhancements On Off] (What's this?)

  • 1. Bender, C. (2003), ``An Itô formula for generalized functionals of a fractional Brownian motion with arbitrary Hurst parameter", Stochastic Process. Appl., 104, 81-106. MR 1956473 (2003m:60137)
  • 2. Biagini, F., Øksendal, B., Sulem, A. and Wallner, N. (2004), ``An introduction to white noise theory and Malliavin calculus for fractional Brownian motion", Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci., 460, 347-372.MR 2052267 (2005a:60107)
  • 3. Elliott, R. J. and Van der Hoek, J., (2003) ``A general fractional white noise theory and applications to finance", Math. Finance, 13, no. 2, 301-339.MR 1967778 (2003m:91077)
  • 4. Hu, Y., Øksendal, B. and Zhang, T. (2004). ``General fractional multiparameter white noise theory and stochastic partial differential equations", Comm. Partial Differential Equations, 29, no. 1-2, 1-23.MR 2038141 (2005b:60174)
  • 5. Tudor, C.A. and Viens, F.G. (2003). `` Itô formula and local time for the fractional Brownian sheet", Electron J. of Probab., 8, no. 14, 1-31.MR 1998763 (2004f:60124)

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Additional Information

Yoon Tae Kim
Affiliation: Department of Statistics, Hallym University, Chuncheon, Kangwon-do 200-702, South Korea

Jong Woo Jeon
Affiliation: Department of Statistics, Seoul National University, Shilim-dong, Kwanak-gu, Seoul 151-742, South Korea

PII: S 0002-9939(06)08466-8
Keywords: Fractional Brownian sheet, It\^o formula, fractional white noise
Received by editor(s): December 17, 2004
Received by editor(s) in revised form: July 5, 2005
Published electronically: June 9, 2006
Additional Notes: This research was supported (in part) by KOSEF through the Statistical Research Center for Complex Systems at Seoul National University, by KOSEF Grant R05-2004-000-11516-0, and by a research grant from Hallym University
Communicated by: Richard C. Bradley
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.