Stochastic integration with respect to fractional Brownian motion;Intégrale stochastique pour le mouvement Brownien fractionaire

Comptes Rendus de l'Academie des Sciences - Series I: Mathematics

Volumn 330, Issue 3, 2000, Pages 231-236

  Carmona, Philippe ^a   Coutin, Laure ^a  

^a INSTITUT DE MATHÉMATIQUES DE TOULOUSE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034134632     PISSN: 07644442     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0764-4442(00)00134-8     Document Type: Article

References (14)

1. [1] Alos E., Mazet O., Nualart D., Stochastic calculus with respect to fractional Brownian motion with Hurst parameter less than 1/2, Tech. report, Universitat de Barcelona, Gran Via 585, 08007 Barcelona, Spain, Mathematic Preprint Series 262, 1999.
2. [2] Carmona Ph., Coutin L., Montseny G., Applications of a representation of long memory Gaussian processes, Tech. Report 06-98, laboratoire de statistique et probabilités, Université Paul-Sabatier, 1998.
3. [3] Dai W., Heyde C.C., Ito's formula with respect to fractional Brownian motion and its application, J. Appl. Math. Stoch. Anal. 9 (4) (1996) 439-448.
4. [4] Decreusefond L., Üstünel A.S., Stochastic analysis of the fractional Brownian motion, Potential Analysis, 1997.
5. [5] Dudley R.M., Norvaisa R., An introduction to p-variation and Young integrals, Tech. Report 1, Maphysto, Centre for Mathematical Physics and Stochastics, University of Aarhus, Denmark, 1998 (Concentrated advanced course).
6. [6] Duncan T.E., Hu Y., Pasik-Duncan B., Stochastic calculus for fractional Brownian motion, I. Theory, Preprint, 1998.
7. [7] Hu Y., Oksendal B., Fractional white noise calculus and applications to finance, preprint, 1999.
8. [8] Lebedev N.N., Special Functions and Their Applications, Dover Publications, New York, 1972 (Translated and edited by Richard A. Silverman).
9. [9] Leon J.A., Fubini theorem for anticipating stochastic integrals in Hilbert space, Appl. Math. and Optim. 27 (1993) 313-327.
10. [10] Lin S.J., Stochastic analysis of fractional Brownian motions, Stoch. Stoch. Rep. 55 (1-2) (1995) 121-140.
11. [11] Nualart D., The Malliavin Calculus and Related Topics, Probability and Its Applications, Springer-Verlag, New York, 1995.
12. [12] Privault N., Skorokhod stochastic integration with respect to non-adapted processes on Wiener space, Stoch. Stoch. Rep. 65 (1-2) (1998) 13-39.
13. [13] Young L.C., An inequality of Hölder type, connected with Stieltjes integration, Acta Math. 67 (1936) 251-282.
14. [14] Zähle M., Integration with respect to fractal functions and Stochastic Calculus, Probab. Th. and Rel. Fields 111 (3) (1998) 333-374.