Results on the Supremum of Fractional Brownian Motion ABSTRACT | FULL TEXT

References (13)

1. Abry, P. and Sellan, F. The wavelet-based synthesis for fractional Brownian motion proposed by F. Sellan and Y. Meyer: Remarks and fast implementation, Appl. Comp. Harmonic Anal., 337–383, 1996.
2. Bertoin, J. Levy Processes (Cambridge University Press,
3. Cambridge, UK, 1996).
4. Biagini, F., Hu, Yaozhong., Oksendal, B. and Zhang, T. Stochastic Calculus for Fractional Brownian Motion and Applications (Springer Verlag, London, 2008).
5. Caglar, M. Simulation of fractional Brownian motion with micropulses, Advances in Per- formance Analysis 3 (1), 43–69, 2000.
6. Decreusefond, L. and Nualart, D. Hitting times For Gaussian processes, Annals Probab., 319–330, 2008.
7. Douady, R., Yor, M. and Shiryaev, A. N. On the probability charateristics of “drop” variables in standard Brownian motion, Theory Probab. Appl. 44 (1), 29–38, 2000.
8. Kolmogorov, A. N. Wienersche Spiralen und einige andere interessante Kurven im Hilbertschen Raum, C. R. (Doklady) Acad. URSS(N.S) 26, 115–118, 1940. L´evy, P. Processus Stochatiques et Mouvement Brownien (Gauthier-Villars, Paris, 1948).
9. Mandelbrot, B. B. and Van Ness, J. W. Fractional Brownian motions, fractional noises and applications, SIAM Rev. 10, 422–437, 1968.
10. Revuz, D. and Yor, M. Continuous Martingales and Brownian Motion (Springer Verlag, Berlin, Hiedelberg, 2001).
11. Rogers, L. C. G. Arbitrage with fractional Brownian motion, Mathematical Finance 7, 95–, 1997.
12. Salminen, P. and Vallois, P. On maximum increase and decrease of Brownian motion, An- nales de l’institut Henri Poincare (B) Probabilit ´Us et Statistiques 43 (6), 655–676, 2007.
13. Sellan, F. Synth´ese de mouvements Browniens fractionaires `a l’aide de la transformation par ondelettes, C. R. Acad. Sci. Paris Ser. Math. 321, 351–358, 1995.