Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
|
   
Available in electronic format
Available in print format 		Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(e) ISSN 0002-9939(p)

     

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
Posted: June 9, 2006
MathSciNet review: 2240682
Full-text PDF Free Access

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

  • 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)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 60H07, 60G18

Retrieve articles in all journals with MSC (2000): 60H07, 60G18

Additional Information

Yoon Tae Kim
Affiliation: Department of Statistics, Hallym University, Chuncheon, Kangwon-do 200-702, South Korea
Email: ytkim@hallym.ac.kr

Jong Woo Jeon
Affiliation: Department of Statistics, Seoul National University, Shilim-dong, Kwanak-gu, Seoul 151-742, South Korea
Email: jwjeon@plaza.snu.ac.kr

DOI: http://dx.doi.org/10.1090/S0002-9939-06-08466-8
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
Posted: 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 after 28 years from publication.




AMS and Social Media LinkedIn Facebook Podcasts Twitter YouTube RSS Feeds Blogs Wikipedia