An extension theorem to rough paths
Annales de l'I.H.P. Analyse non linéaire, Tome 24 (2007) no. 5, pp. 835-847. 
@article{AIHPC_2007__24_5_835_0,
     author = {Lyons, Terry and Victoir, Nicolas},
     title = {An extension theorem to rough paths},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {835--847},
     publisher = {Elsevier},
     volume = {24},
     number = {5},
     year = {2007},
     doi = {10.1016/j.anihpc.2006.07.004},
     mrnumber = {2348055},
     zbl = {1134.60047},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1016/j.anihpc.2006.07.004/}
}
TY  - JOUR
AU  - Lyons, Terry
AU  - Victoir, Nicolas
TI  - An extension theorem to rough paths
JO  - Annales de l'I.H.P. Analyse non linéaire
PY  - 2007
SP  - 835
EP  - 847
VL  - 24
IS  - 5
PB  - Elsevier
UR  - http://archive.numdam.org/articles/10.1016/j.anihpc.2006.07.004/
DO  - 10.1016/j.anihpc.2006.07.004
LA  - en
ID  - AIHPC_2007__24_5_835_0
ER  - 
%0 Journal Article
%A Lyons, Terry
%A Victoir, Nicolas
%T An extension theorem to rough paths
%J Annales de l'I.H.P. Analyse non linéaire
%D 2007
%P 835-847
%V 24
%N 5
%I Elsevier
%U http://archive.numdam.org/articles/10.1016/j.anihpc.2006.07.004/
%R 10.1016/j.anihpc.2006.07.004
%G en
%F AIHPC_2007__24_5_835_0
Lyons, Terry; Victoir, Nicolas. An extension theorem to rough paths. Annales de l'I.H.P. Analyse non linéaire, Tome 24 (2007) no. 5, pp. 835-847. doi : 10.1016/j.anihpc.2006.07.004. http://archive.numdam.org/articles/10.1016/j.anihpc.2006.07.004/

[1] Bass R.F., Hambly B.M., Lyons T.J., Extending the Wong-Zakai theorem to reversible Markov processes, J. Eur. Math. Soc. 4 (2002) 237-269. | Zbl

[2] Capitaine M., Donati-Martin C., The Lévy area process for the free Brownian motion, J. Funct. Anal. 179 (1) (2001) 153-169. | MR | Zbl

[3] Coutin L., Qian Z., Stochastic analysis, rough path analysis and fractional Brownian motions, Probab. Theory Related Fields 122 (1) (2002) 108-140. | MR | Zbl

[4] Doss H., Liens entre équations différentielles stochastiques et ordinaires, Ann. Inst. H. Poincaré 13 (1977) 99-125. | Numdam | MR | Zbl

[5] Folland G.B., Stein E.M., Hardy spaces on homogeneous groups, Math. Notes 28 (1982). | MR | Zbl

[6] P. Friz, N. Victoir, On the notion of geometric rough paths, preprint, 2004.

[7] Gromov M., Carnot-Caratheodory spaces seen from within, in: Bellaiche A., Risler J.-J. (Eds.), Sub-Riemannian Geometry, Progress in Mathematics, vol. 144, Birkhäuser, 1996, pp. 79-323. | Zbl

[8] Hambly B.M., Lyons T.J., Stochastic area for Brownian motion on the Sierpinski gasket, Ann. Probab. 26 (1) (1998) 132-148. | MR | Zbl

[9] Karatzas I., Shreve S.E., Brownian Motion and Stochastic Calculus, Graduate Texts in Mathematics, vol. 113, second ed., Springer-Verlag, New York, 1991. | MR | Zbl

[10] Ledoux M., Lyons T., Qian Z., Lévy area of Wiener processes in Banach spaces, Ann. Probab. 30 (2) (2002) 546-578. | MR | Zbl

[11] Lejay A., Introduction to Rough Paths, Séminaire de probabilités, Lecture Notes in Mathematics, vol. XXXVII, 2003. | MR | Zbl

[12] Lyons T., Differential equations driven by rough signals, Rev. Mat. Iberoamericana 14 (2) (1998) 215-310. | MR | Zbl

[13] Lyons T., Qian Z., System Control and Rough Paths, Oxford University Press, 2002. | MR | Zbl

[14] Reutenauer C., Free Lie Algebras, London Mathematical Society Monographs (N.S.), vol. 7, Oxford Science Publications, 1993. | MR | Zbl

[15] Serre J.P., Lie Algebras and Lie Groups, Lecture Notes in Mathematics, vol. 1500, 1992. | MR | Zbl

[16] Sussman H.J., On the gap between deterministic and stochastic ordinary differential equations, Ann. Probab. 6 (1978) 19-41. | MR | Zbl

[17] Varadarajan V.S., Lie Groups, Lie Algebras, and their Representations, Graduate Texts in Mathematics, vol. 102, 1984. | MR | Zbl

[18] N.B. Victoir, Levy area for the free Brownian motion: existence and non-existence, J. Funct. Anal., in press. | Zbl

Cité par Sources :