Self-similarity and fractional Brownian motions on lie groups

Electronic Journal of Probability

Volumn 13, Issue , 2008, Pages 1120-1139

  Coutin, Laure ^b  

^a INSTITUT DE MATHÉMATIQUES DE TOULOUSE   (France)

^b UNIVERSITÉ PARIS DESCARTES   (France)

Author keywords

Fractional Brownian motion; Lie group

Indexed keywords

EID: 48449083110     PISSN: None     EISSN: 10836489     Source Type: Journal    
DOI: 10.1214/EJP.v13-530     Document Type: Article

References (31)

1. F. Baudoin: An Introduction to the Geometry of Stochastic Flows, Imperial College Press, (2004).
2. F. Baudoin, L. Coutin: Operators associated with a stochastic differential equation driven by fractional Brownian motions, Stochastic Processes and their Applications (2007).
3. G. Ben Arous: Flots et series de Taylor stochastiques, Probab. Theory Relat. Fields, 81, 29-77, (1989).
4. C. Borell, On polynomial chaos and integrability, Probab. Math. Statis. (3) (1984) 191-203.
5. F. Castell: Asymptotic expansion of stochastic flows, Probab. Theory Relat. Fields, 96, 225-239, (1993).
6. P. Cheridito and D. Nualart: Stochastic integral of divergence type with respect to fractional Brownian motion with Hurst parameter H in (0,1/2), preprint.
7. L. Coutin, P Friz and N. Victoir, Good Rough Path Sequences ans Applications to Anticipating and Fractional Stochastic Calculus; preprint 2005
8. L. Coutin, Z. Qian: Stochastic rough path analysis and fractional Brownian motion, Probab. Theory Relat. Fields 122, 108-140, (2002).
9. L. Decreusefond and A. S. Ustunel, Stochastic analysis of the fractional Brownian motion, Potential Analysis. 10, 177-214, (1998).
10. Friz P., Victoir N. (2006): Euler estimates for rough differential equations, preprint.
11. M. Gradinaru, I. Nourdin, F. Russo, P. Vallois: m-order integrals and generalized Ito's formula: the case of fractional Brownian motion with any Hurst parameter, To appear in Ann. Inst. H. Poincare.
12. Hunt G.A.: Markov processes and potentials: I,II,III, Illinois J. Math, 1, 44-93, 316-369 (1957); 2, 151-213, (1958).
13. K. Ito: Stochastic differential equations on a manifold, Nagoya Math. Journal, 1, 35-47, (1950).
14. H. Kunita, Stochastic flows with self-similar properties, Stochastic analysis and applications (ed. by Davies, Truman and Elworthy), World Scientific, 286-300, (1996).
15. H. Kunita, Asymptotic Self-Similarity and Short Time Asymptotics of Stochastic Flows, J. Math. Sci. Univ. Tokyo, 4, 595-619, (1997).
16. W. Lawton: Infinite convolution products and refinable distributions on Lie groups, Trans. Am. Math. Soc., Vol. 352, 6, 2913-2936, (2000).
17. A. Lejay: An introduction to Rough paths, séminaire de probabilités XXXVII (2003), Vol. 1832 of Lectures Notes in Mathematics, pp1-59, Springer-Verlag.
18. X.D. Li, T. Lyons: Smoothness of Ito maps and simulated annealing on path spaces (I), 1 < p < 2, preprint, 2003.
19. T. Lyons, Differential Equations Driven by Rough Signals, Revista Mathematica Iberio Americana, Vol 14, No 2, 215 - 310, (1998).
20. T. Lyons, Z. Qian, System Control and Rough Paths, Oxford Science Publications, (2002)
21. P. Malliavin, Stochastic Analysis, Grundlehren der mathematischen Wissenschaften, Vol. 313, Springer, (1997).
22. Nourdin, Ivan, Schemas d'approximation associes à une equation differentielle dirigee par une fonction holderienne; cas du mouvement brownien fractionnaire, C. R. Math. Acad. Sci. Paris 340, (2005), 8, p 611-614.
23. I. Nourdin, C. Tudor: Remarks on some linear fractional stochastic equations, preprint, (2005).
24. D. Nualart and A. Rascanu: Differential equations driven by fractional Brownian motion, Collect. Math. 53, 1, 55-81,(2002).
25. D. Nualart, B. Saussereau: Malliavin calculus for stochastic differential equation driven by a fractional Brownian motion, preprint.
26. Rogers L.C.G., Williams D.: Diffusions, Markov processes and Martingales, Vol. 2, second edition, Cambridge university press, (2000).
27. R.S. Strichartz: The Campbell-Baker-Hausdorff-Dynkin formula and solutions of differential equations, Jour. Func. Anal., 72, 320-345, (1987).
28. Y. Yamato: Stochastic differential equations and nilpotent Lie algebras. Z. Wahrscheinlichkeitstheorie. Verw. Geb., 47, 213-229, (1979).
29. Yosida K.: Brownian motion in homogeneous Riemannian space, Pacific J. Math., 2, 263-296, (1952).
30. Young L.C. (1936): An inequality of the Hôlder type connected with Stieltjes integration. Acta Math., 67, 251-282.
31. Zôhle, M. (2001) Integration with respect to fractal functions and stochastic calculus. II, Math. Nachr. Mathematische Nachrichten, 225, 145-183.