Smoothness of Itô maps and diffusion processes on path spaces (I)

Xiang-Dong Li; Terry J. Lyons

Annales scientifiques de l'École Normale Supérieure (2006)

  • Volume: 39, Issue: 4, page 649-677
  • ISSN: 0012-9593

How to cite

top

Li, Xiang-Dong, and Lyons, Terry J.. "Smoothness of Itô maps and diffusion processes on path spaces (I)." Annales scientifiques de l'École Normale Supérieure 39.4 (2006): 649-677. <http://eudml.org/doc/82697>.

@article{Li2006,
author = {Li, Xiang-Dong, Lyons, Terry J.},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {rough paths; Itô map; fractional like Brownian motion},
language = {eng},
number = {4},
pages = {649-677},
publisher = {Elsevier},
title = {Smoothness of Itô maps and diffusion processes on path spaces (I)},
url = {http://eudml.org/doc/82697},
volume = {39},
year = {2006},
}

TY - JOUR
AU - Li, Xiang-Dong
AU - Lyons, Terry J.
TI - Smoothness of Itô maps and diffusion processes on path spaces (I)
JO - Annales scientifiques de l'École Normale Supérieure
PY - 2006
PB - Elsevier
VL - 39
IS - 4
SP - 649
EP - 677
LA - eng
KW - rough paths; Itô map; fractional like Brownian motion
UR - http://eudml.org/doc/82697
ER -

References

top
  1. [1] Andersson L., Driver B.K., Finite-dimensional approximations to Wiener measure and path integral formulas on manifolds, J. Funct. Anal.165 (2) (1999) 430-498. Zbl0943.58024MR1698956
  2. [2] Cartan E., Leçons sur la géométrie projective complexe, Les Grands Classiques Gauthier-Villars, 1931. Zbl0003.06801MR41456
  3. [3] Cartan E., La théorie des groupes finis et continus et la géométrie différentielle traitées par la méthode du repère mobile, Les Grands Classiques Gauthier-Villars, 1937. Zbl63.1227.02
  4. [4] Cartan E., Leçons sur la théorie des espaces à connexion projective, Les Grands Classiques Gauthier-Villars, 1937. Zbl0016.07603JFM63.0689.05
  5. [5] Coutin L., Qian Z., Stochastic analysis, rough path analysis and fractional Brownian motions, Probab. Theory Related Fields122 (1) (2002) 108-140. Zbl1047.60029MR1883719
  6. [6] Dieudonné J., Foundations of Mordern Analysis, vol. I, Academic Press, New York, 1969. Zbl0176.00502MR349288
  7. [7] Driver B.K., A Cameron–Martin type quasi-invariance theorem for Brownian motion on a compact manifold, J. Funct. Anal.109 (1992) 272-376. Zbl0765.60064MR1194990
  8. [8] Driver B.K., Integration by parts and quasi-invariance for heat kernel measures on loop groups, J. Funct. Anal.149 (2) (1997) 470-547. Zbl0887.58062MR1472366
  9. [9] Dudley R.M., Norvaisa R., Differentiability of Six Operators on Nonsmooth Functions and p-Variation, Lecture Notes in Math., vol. 1703, Springer, Berlin, 1999. Zbl0973.46033MR1705318
  10. [10] Eells J., Elworthy K.D., Wiener integration on certain manifolds, in: Problems in Non-Linear Analysis (C.I.M.E., IV Ciclo, Varenna, 1970), Edizioni Cremonese, Rome, 1971, pp. 67-94. Zbl0226.58007MR346835
  11. [11] Itô K., The Brownian motion and tensor fields on Riemannian manifold, in: International Congress of Mathematicians 1963 (Stocholm), Inst. Mittag-Leffler, Djursholm, pp. 536–539. Zbl0116.36105MR176500
  12. [12] Klingenberg W., Lectures on Closed Geodesics, Springer, Berlin, 1978. Zbl0397.58018MR478069
  13. [13] Li X.D., Stochastic analysis and geometry on path and loop spaces, PhD thesis, Academia Sinica (Beijing) and University of Lisbon, 1999. 
  14. [14] Li X.D., Existence and uniqueness of geodesics on path spaces, J. Funct. Anal.173 (2000) 182-202. Zbl0956.58018MR1760282
  15. [15] Li X.D., Connections, geodesics and measures on path and loop spaces, Preprint, 2002. 
  16. [16] Li X.D., Sobolev spaces and capacities theory on path spaces over a compact Riemannian manifold, Probab. Theory Related Fields125 (1) (2003) 96-134. Zbl1018.58026MR1952459
  17. [17] Lyons T., Differential equations driven by rough signals. I. An extension of an inequality of L.C. Young, Math. Res. Lett.1 (4) (1994) 451-464. Zbl0835.34004MR1302388
  18. [18] Lyons T., Differential equations driven by rough signals, Revista Matemática Iberoamericana14 (2) (1998) 215-300. Zbl0923.34056MR1654527
  19. [19] Ledoux M., Lyons T., Qian Z., Lévy area of Wiener processes in Banach spaces, Ann. Probab.30 (2) (2002) 546-578. Zbl1016.60071MR1905851
  20. [20] Lyons T., Qian Z., A class of vector fields on path space, J. Funct. Anal.145 (1) (1997) 205-223. Zbl0877.58059MR1442166
  21. [21] Lyons T., Qian Z., Stochastic Jacobi fields and vector fields induced by varying area on path spaces, Probab. Theory Related Fields109 (4) (1997) 539-570. Zbl0903.60008MR1483599
  22. [22] Lyons T., Qian Z., System Control and Rough Paths, Oxford Mathematical Monographs, Clarendon Press, Oxford, 2002. Zbl1029.93001MR2036784
  23. [23] Malliavin P., Hypoellipticity in infinite dimensions, in: Diffusion processes and related problems in analysis, vol. I (Evanston, IL, 1989), Birkhäuser Boston, 1990, pp. 17-31. Zbl0723.60059MR1110154
  24. [24] Malliavin P., Stochastic Analysis, Springer, Berlin, 1997. Zbl0878.60001MR1450093
  25. [25] Stein E.M., Singular Integrals and Differentiability Properties of Functions, Princeton Mathematical Series, vol. 30, Princeton University Press, Princeton, NJ, 1970. Zbl0207.13501MR290095

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.