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

Li, Xiang-Dong; Lyons, Terry J.

doi:10.1016/j.ansens.2006.07.001

Li, Xiang-Dong ; Lyons, Terry J.

Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 39 (2006) no. 4, pp. 649-677.

MR Zbl

DOI : 10.1016/j.ansens.2006.07.001

@article{ASENS_2006_4_39_4_649_0,
     author = {Li, Xiang-Dong and Lyons, Terry J.},
     title = {Smoothness of {It\^o} maps and diffusion processes on path spaces {(I)}},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     pages = {649--677},
     publisher = {Elsevier},
     volume = {Ser. 4, 39},
     number = {4},
     year = {2006},
     doi = {10.1016/j.ansens.2006.07.001},
     mrnumber = {2290140},
     zbl = {05125022},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.ansens.2006.07.001/}
}

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Li, Xiang-Dong; Lyons, Terry J. Smoothness of Itô maps and diffusion processes on path spaces (I). Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 39 (2006) no. 4, pp. 649-677. doi : 10.1016/j.ansens.2006.07.001. http://www.numdam.org/articles/10.1016/j.ansens.2006.07.001/

Bibliographie
Cité par

[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. | MR | Zbl

[2] Cartan E., Leçons sur la géométrie projective complexe, Les Grands Classiques Gauthier-Villars, 1931. | MR | Zbl

[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.

[4] Cartan E., Leçons sur la théorie des espaces à connexion projective, Les Grands Classiques Gauthier-Villars, 1937. | JFM | Zbl

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

[6] Dieudonné J., Foundations of Mordern Analysis, vol. I, Academic Press, New York, 1969. | MR | Zbl

[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. | MR | Zbl

[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. | MR | Zbl

[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. | MR | Zbl

[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. | MR | Zbl

[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. | MR | Zbl

[12] Klingenberg W., Lectures on Closed Geodesics, Springer, Berlin, 1978. | MR | Zbl

[13] Li X.D., Stochastic analysis and geometry on path and loop spaces, PhD thesis, Academia Sinica (Beijing) and University of Lisbon, 1999.

[14] Li X.D., Existence and uniqueness of geodesics on path spaces, J. Funct. Anal. 173 (2000) 182-202. | MR | Zbl

[15] Li X.D., Connections, geodesics and measures on path and loop spaces, Preprint, 2002.

[16] Li X.D., Sobolev spaces and capacities theory on path spaces over a compact Riemannian manifold, Probab. Theory Related Fields 125 (1) (2003) 96-134. | MR | Zbl

[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. | MR | Zbl

[18] Lyons T., Differential equations driven by rough signals, Revista Matemática Iberoamericana 14 (2) (1998) 215-300. | MR | Zbl

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

[20] Lyons T., Qian Z., A class of vector fields on path space, J. Funct. Anal. 145 (1) (1997) 205-223. | MR | Zbl

[21] Lyons T., Qian Z., Stochastic Jacobi fields and vector fields induced by varying area on path spaces, Probab. Theory Related Fields 109 (4) (1997) 539-570. | MR | Zbl

[22] Lyons T., Qian Z., System Control and Rough Paths, Oxford Mathematical Monographs, Clarendon Press, Oxford, 2002. | MR | Zbl

[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. | MR | Zbl

[24] Malliavin P., Stochastic Analysis, Springer, Berlin, 1997. | MR | Zbl

[25] Stein E.M., Singular Integrals and Differentiability Properties of Functions, Princeton Mathematical Series, vol. 30, Princeton University Press, Princeton, NJ, 1970. | MR | Zbl

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