Stochastic Analysis of the Fractional Brownian Motion

Potential Analysis

Volumn 10, Issue 2, 1999, Pages 177-214

  Decreusefond, L ^a   Ustunel A S ^a  

^a TELECOM PARISTECH   (France)

Author keywords

Fractional Brownian motion; Girsanov formula; It formula; Stochastic calculus of variations

Indexed keywords

EID: 0042637937     PISSN: 09262601     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1008634027843     Document Type: Article

References (17)

1. Arcones, M.A.: 'On the law of the iterated logarithm for Gaussian processes', Journal of Theoretical Probability 8(4) (1995), 877-904.
2. Barton, R.J. and Vincent Poor, H.: 'Signal detection in fractional Gaussian noise', IEEE Trans. on Information Theory 34 (5) (1988), 943-959.
3. Bertoin, J.: 'Sur un intégrale pour les processus à a variation bornée', The Annals of Probability 17(4) (1989), 1521-1535.
4. Bouleau, N. and Hirsch, F.: Dirichlet Forms and Analysis on Wiener Space, De Gruyter Studies in Mathematics, Berlin, New York, 1992.
5. Coelho, R. and Decreusefond, L.: 'Smoothed video trafic modelling for statistical multiplexing analysis', in: Kouvatsos D. (ed.), Sixth IFIP Workshop on Performance Modelling and Evaluation of ATM Networks, Chapman & Hall, London, 1995.
6. Feyel, D. and de La Pradelle, A.: Fractional integrals and Brownian processes, Preprint, Université d'Évry, 1996, 1996.
7. Föllmer, H.: 'Calcul d'Itô sans probabilité', in: Azema J. (ed.) Séminaire de probabilités, Springer-Verlag, 1980, pp. 143-150.
8. Leland, W.E., Taqqu, M.S., Willinger, W. and Wilson, D.V.: 'On the self-similar nature of ethernet traffic', IEEE/ACM Trans. Networking 2(1) (1994), 1-15.
9. Lin, S.J.: Stochastic analysis of fractional Brownian motions. To appear in Stochastics, 1996, 1996.
10. Mandelbrot, B. and Van Ness, J.: 'Fractional Brownian motions, fractional noises and applications', SIAM Review 10(4) (1968), 422-437.
11. Nikiforov, A.F. and Uvarov, V.B.: Special Functions of Mathematical Physics, Birkhäuser, Boston, 1988.
12. Norros, I.: 'On the use of the fractional Brownian motion in the theory of connectionless networks', IEEE Jour. on Sel. Ar. in Communications 13(6) (1995), 953-962.
13. Samko, S.G., Kilbas, A.A. and Marichev, O.I.: Fractional Integrals and Derivatives, Gordon and Breach Science, 1993.
14. Üstünel, A.S.: 'The Itô formula for anticipative processes with non-monotonous time scale via the Malliavin calculus', Probability Theory and Related Fields 79 (1988), 249-269.
15. Üstünel, A.S.: An Introduction to Analysis on Wiener Space, Lectures Notes in Mathematics 1610, Springer-Verlag, 1995.
16. Üstünel, A.S. and Zakai, M.: 'The constructions of filtrations on abstract Wiener spaces', Journal of Funct. Analysis 143(1) 1997.
17. Watanabe, S.: Lectures on Stochastic Differential Equations and Malliavin Calculus Tata Institute of Fundamental Research, 1984.