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http://dx.doi.org/10.4134/CKMS.2011.26.4.669

THE LAW OF A STOCHASTIC INTEGRAL WITH TWO INDEPENDENT BIFRACTIONAL BROWNIAN MOTIONS  

Liu, Junfeng (School of Mathematics and Statistics Nanjing Audit University)
Publication Information
Communications of the Korean Mathematical Society / v.26, no.4, 2011 , pp. 669-684 More about this Journal
Abstract
In this note, we obtain the expression of the characteristic fucntion of the random variable $\int_o^TB_s^{{\alpha},{\beta}}dB_s^{H,K}$, where $B^{{\alpha},{\beta}}$ and $B^{H,K}$ are two independent bifractional Brownian motions with indices ${\alpha}{\in}(0,1),{\beta}{\in}(0, 1]$ and $HK{\in}(\frac{1}{2},\;1)$ respectively.
Keywords
bifractional Brownian motion; stochastic integral; characteristic function;
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1 P. E. Protter, Stochastic Integration and Differential Equations, Springer-Verlag, Berlin, 2005.
2 F. Russo and C. A. Tudor, On bifractional Brownian motion, Stochastic Process. Appl. 116 (2006), no. 5, 830-856.   DOI   ScienceOn
3 C. A. Tudor and Y. Xiao, Sample path properties of bifractional Brownian motion, Bernoulli 13 (2007), no. 4, 1023-1052.   DOI   ScienceOn
4 L. Yan, J. Liu, and G. Jing, Quadratic covariation and Ito formula for a bifractional Brownian motion, preprint (2008).
5 M. Yor, Remarques sur une formule de Paul Levy, pp. 343-346, Lecture Notes in Math., 784, Springer, Berlin, 1980.   DOI
6 F. Biagini, Y. Hu, B. Oksendal, and T. Zhang, Stochastic Calculus for Fractional Brow- nian Motion and Applications, Springer-Verlag London, Ltd., London, 2008.
7 P. Caithamer, Decoupled double stochastic fractional integrals, Stochastics 77 (2005), no. 3, 205-210.   DOI
8 K. Es-Sebaiy and C. A. Tudor, Multidimensional bifractional Brownian motion: Ito and Tanaka formulas, Stoch. Dyn. 7 (2007), no. 3, 365-388.   DOI   ScienceOn
9 I. Kruk, F. Russo, and C. A. Tudor, Wiener integrals, Malliavin calculus and covariance measure structure, J. Funct. Anal. 249 (2007), no. 1, 92-142.   DOI   ScienceOn
10 C. Houdre and J. Villa, An example of infinite dimensional quasi-helix, Stochastic models (Mexico City, 2002), 195-201, Contemp. Math., 336, Amer. Math. Soc., Providence, RI, 2003.   DOI
11 Y. Hu, Integral transformations and anticipative calculus for fractional Brownian motions, Mem. Amer. Math. Soc. 175 (2005), no. 825, viii+127 pp.
12 R. Klein and E. Gine, On quadratic variation of processes with Gaussian increments, Ann. Probab. 3 (1975), no. 4, 716-721.   DOI   ScienceOn
13 P. Lei and D. Nualart, A decomposition of the bifractional Brownian motion and some applications, Statist. Probab. Lett. 79 (2009), no. 5, 619-624.   DOI   ScienceOn
14 R. Berthuet, Loi du logharitme itere pour cetaines integrales stochastiques, Ann. Sci. Univ. Clermont-Ferrand Math. 69 (1981), 9-18.
15 P. Levy, Wiener's random function, and other Laplacian random functions, Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability, 1950, pp. 171-187. University of California Press, Berkeley and Los Angeles, 1951.
16 Y. Mishura, Stochastic Calculus for Fractional Brownian Motion and Related Processes, Lecture Notes in Mathematics, 1929. Springer-Verlag, Berlin, 2008.
17 D. Nualart, Malliavin Calculus and Related Topics, 2nd edition Springer, New York, 2006.
18 E. Alos, O. Mazet, and D. Nualart, Stochastic calculus with respect to Gaussian pro- cesses, Ann. Probab. 29 (2001), no. 2, 766-801.   DOI   ScienceOn
19 X. Bardina and C. A. Tudor, The law of a stochastic integral with two independent fractional Brownian motions, Bol. Soc. Mat. Mexicana (3) 13 (2007), no. 1, 231-242.