An extension theorem to rough paths

Terry Lyons; Nicolas Victoir

Annales de l'I.H.P. Analyse non linéaire (2007)

  • Volume: 24, Issue: 5, page 835-847
  • ISSN: 0294-1449

How to cite

top

Lyons, Terry, and Victoir, Nicolas. "An extension theorem to rough paths." Annales de l'I.H.P. Analyse non linéaire 24.5 (2007): 835-847. <http://eudml.org/doc/78762>.

@article{Lyons2007,
author = {Lyons, Terry, Victoir, Nicolas},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {rough paths; differential equations; -variation; continuity},
language = {eng},
number = {5},
pages = {835-847},
publisher = {Elsevier},
title = {An extension theorem to rough paths},
url = {http://eudml.org/doc/78762},
volume = {24},
year = {2007},
}

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
PB - Elsevier
VL - 24
IS - 5
SP - 835
EP - 847
LA - eng
KW - rough paths; differential equations; -variation; continuity
UR - http://eudml.org/doc/78762
ER -

References

top
  1. [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. Zbl1010.60070
  2. [2] Capitaine M., Donati-Martin C., The Lévy area process for the free Brownian motion, J. Funct. Anal.179 (1) (2001) 153-169. Zbl0979.60044MR1807256
  3. [3] Coutin L., Qian Z., Stochastic analysis, rough path analysis and fractional Brownian motions, Probab. Theory Related Fields122 (1) (2002) 108-140. Zbl1047.60029MR1883719
  4. [4] Doss H., Liens entre équations différentielles stochastiques et ordinaires, Ann. Inst. H. Poincaré13 (1977) 99-125. Zbl0359.60087MR451404
  5. [5] Folland G.B., Stein E.M., Hardy spaces on homogeneous groups, Math. Notes28 (1982). Zbl0508.42025MR657581
  6. [6] P. Friz, N. Victoir, On the notion of geometric rough paths, preprint, 2004. Zbl1108.34052
  7. [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. Zbl0864.53025
  8. [8] Hambly B.M., Lyons T.J., Stochastic area for Brownian motion on the Sierpinski gasket, Ann. Probab.26 (1) (1998) 132-148. Zbl0936.60073MR1617044
  9. [9] Karatzas I., Shreve S.E., Brownian Motion and Stochastic Calculus, Graduate Texts in Mathematics, vol. 113, second ed., Springer-Verlag, New York, 1991. Zbl0734.60060MR1121940
  10. [10] Ledoux M., Lyons T., Qian Z., Lévy area of Wiener processes in Banach spaces, Ann. Probab.30 (2) (2002) 546-578. Zbl1016.60071MR1905851
  11. [11] Lejay A., Introduction to Rough Paths, Séminaire de probabilités, Lecture Notes in Mathematics, vol. XXXVII, 2003. Zbl1041.60051MR2053040
  12. [12] Lyons T., Differential equations driven by rough signals, Rev. Mat. Iberoamericana14 (2) (1998) 215-310. Zbl0923.34056MR1654527
  13. [13] Lyons T., Qian Z., System Control and Rough Paths, Oxford University Press, 2002. Zbl1029.93001MR2036784
  14. [14] Reutenauer C., Free Lie Algebras, London Mathematical Society Monographs (N.S.), vol. 7, Oxford Science Publications, 1993. Zbl0798.17001MR1231799
  15. [15] Serre J.P., Lie Algebras and Lie Groups, Lecture Notes in Mathematics, vol. 1500, 1992. Zbl0742.17008MR1176100
  16. [16] Sussman H.J., On the gap between deterministic and stochastic ordinary differential equations, Ann. Probab.6 (1978) 19-41. Zbl0391.60056MR461664
  17. [17] Varadarajan V.S., Lie Groups, Lie Algebras, and their Representations, Graduate Texts in Mathematics, vol. 102, 1984. Zbl0955.22500MR746308
  18. [18] N.B. Victoir, Levy area for the free Brownian motion: existence and non-existence, J. Funct. Anal., in press. Zbl1062.46055

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.