论文信息 - Stochastic Analysis of the Fractional Brownian Motion

Stochastic Analysis of the Fractional Brownian Motion

Since the fractional Brownian motion is not a semiimartingale, the usual Ito calculus cannot be used to deene a full stochastic calculus. However, in this work, we obtain the Itt formula, the ItttClark representation formula and the Girsanov theorem for the functionals of a fractional Brownian motion using the stochastic calculus of variations.

A. S. ÜstünelÉcole

[1] B. Mandelbrot,et al. Fractional Brownian Motions, Fractional Noises and Applications , 1968 .

[2] Shinzo Watanabe. Lectures on stochastic di erential equations and Malliavin calculus , 1979 .

[3] H. Vincent Poor,et al. Signal detection in fractional Gaussian noise , 1988, IEEE Trans. Inf. Theory.

[4] The Itô formula for anticipative processes with nonmonotonous time scale via the Malliavin Calculus , 1988 .

[5] Nicolas Bouleau,et al. Dirichlet Forms and Analysis on Wiener Space , 1991 .

[6] Murad S. Taqqu,et al. On the Self-Similar Nature of Ethernet Traffic , 1993, SIGCOMM.

[7] Ilkka Norros,et al. On the Use of Fractional Brownian Motion in the Theory of Connectionless Networks , 1995, IEEE J. Sel. Areas Commun..

[8] M. A. Arcones,et al. On the law of the iterated logarithm for Gaussian processes , 1995 .

[9] S. J. Lin,et al. Stochastic analysis of fractional brownian motions , 1995 .

[10] Denis Feyel,et al. Fractional Integrals And Brownian Processes , 1996 .