[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.5351/CKSS.2010.17.1.047

A Note on the Wick Integral with Respect to Fractional Brownian Sheet

Rhee, Joon-Hee (Department of Business and Administration, Soong-Sil University)
Kim, Yoon-Tae (Department of Statistics, Hallym University)

Publication Information

Communications for Statistical Applications and Methods / v.17, no.1, 2010 , pp. 47-54 More about this Journal

Abstract

By using the white noise theory for fractional Brownian sheet, we give new representations of the Wick integrals of various types with respect to fractional Brownian sheet with Hurst parameters $H_1,H_2{\in}$ (0, 1).

Keywords

Fractional Brownian sheet; white noise theory; stochastic line integral; wick integrals; wick product;

Citations & Related Records

Times Cited By KSCI : 2 (Citation Analysis)

Reference
Cited By KSCI

1	Kim, Y. T. and Park, H. S. (2009). Stratonovich calculus with respect to fractional Brownian sheet, Stochastic Analysis and Applications, 27, 1-22. DOI ScienceOn
2	Kim, Y. T. and Rhee, J. (2008). A note on Ito formula for a fractional Brownian sheet with Hurst parameters $H_1,\;H_2\;{\epsilon}$ (0, 1), Journal of the Korean Statistical Society, 37, 349-354. DOI ScienceOn
3	Tudor, C. A. and Viens, F. G. (2003). Ito Formula and Local Time for the Fractional Brownian Sheet, Electronic Journal of Probability, 8, 1-31.
4	Biagini, F., Oksendal, B., Sulem, A. and Wallner, N. (2004). An introduction to white noise theory and Malliavin calculus for fractional Brownian motion, Proceedings: Mathematical, Physical and Engineering Sciences, 460, 347-372. DOI ScienceOn
5	Cairoli, R. and Walsh, J. B. (1975). Stochastic integrals in the plane, Acta Mathematica, 134, 111-183. DOI
6	Elliott, R. J. and van der Hoek, J. (2003). A general fractional white noise theory and applications to finance, Mathematical Finance, 13, 301-339. DOI ScienceOn
7	Kim, Y. T. (2009). A note on the differentiation formula in Stratonovich type for a fractional Brownian sheet, Journal of the Korean Statistical Society, 38, 259-265. DOI ScienceOn
8	Holden, H., Oksendal, B., Uboe, J. and Zhang, T. (1996). Stochastic Partial Differential Equations, Birkhauser, Boston.
9	Hu, Y., Oksendal, B. and Zhang, T. (2004). General fractional multiparameter white noise theory and stochastic partial differential equations, Communications in Partial Differential Equations, 29, 1-23. DOI ScienceOn
10	Kim, Y. T. (2006). An Ito formula of generalized functionals and local time for fractional Brownian sheet, Stochastic Analysis and Applications, 24, 973-997. DOI ScienceOn
11	Kim, Y. T. and Jeon, J. W. (2006). An Ito formula for a fractional Brownian sheet with arbitrary Hurst parameters, Proceedings of the American Mathematical Society, 134, 3677-3683. DOI ScienceOn
12	Kim, Y. T., Jeon, J. W. and Park, H. S. (2008). Various types of stochastic integrals with respect to fractional Brownian sheet and their applications, Journal of Mathematical Analysis and Applications, 341, 1382-1398. DOI ScienceOn
13	Kim, Y. T., Jeon, J. W. and Park, H. S. (2009). Differentiation formula in Stratonovich version for fractional Brownian sheet, Journal of Mathematical Analysis and Applications, 359, 106-125. DOI ScienceOn