S. Aida, Gradient Estimates of Harmonic Functions and the Asymptotics of Spectral Gaps on Path Spaces., Interdisciplinary Information Sciences, vol.2, issue.1, pp.75-84, 1996.
DOI : 10.4036/iis.1996.75

S. Aida and D. Elworthy, Differential calculus on path and loop spaces I. logarithmic Sobolev inequalities on path spaces, C. R. Acad. Sci. Paris, pp.321-97, 1995.

D. Bakry and M. Emery, Diffusions hypercontractives, Sém. de Probab., XIX, Lect. Notes in Math, vol.1123, pp.177-206, 1985.
DOI : 10.1007/BFb0075847

URL : http://archive.numdam.org/article/SPS_1985__19__177_0.pdf

D. Bakry and M. Ledoux, A logarithmic Sobolev form of the Li-Yau parabolic inequality, Revista Matem??tica Iberoamericana, vol.22, pp.683-702, 2006.
DOI : 10.4171/RMI/470

URL : https://hal.archives-ouvertes.fr/hal-00353946

J. M. Bismut, Large deviation and Malliavin Calculus, 1984.

B. Capitaine, E. P. Hsu, and M. Ledoux, Martingale Representation and a Simple Proof of Logarithmic Sobolev Inequalities on Path Spaces, Electronic Communications in Probability, vol.2, issue.0, pp.71-81, 1997.
DOI : 10.1214/ECP.v2-986

A. B. Cruzeiro and P. Malliavin, Renormalized Differential Geometry on Path Space: Structural Equation, Curvature, Journal of Functional Analysis, vol.139, issue.1, pp.119-181, 1996.
DOI : 10.1006/jfan.1996.0081

A. B. Cruzeiro and S. Fang, Weak Levi-Civita Connection for the Damped Metric on the Riemannian Path Space and Vanishing of Ricci Tensor in Adapted Differential Geometry, Journal of Functional Analysis, vol.185, issue.2, pp.681-698, 2001.
DOI : 10.1006/jfan.2001.3765

B. Driver, A Cameron-Martin type quasi-invariance theorem for Brownian motion on a compact Riemannian manifold, Journal of Functional Analysis, vol.110, issue.2, pp.272-376, 1992.
DOI : 10.1016/0022-1236(92)90035-H

D. Elworthy and X. M. Li, Formulae for the Derivatives of Heat Semigroups, Journal of Functional Analysis, vol.125, issue.1, pp.252-287, 1994.
DOI : 10.1006/jfan.1994.1124

K. D. Elworthy, Y. Le-jan, and X. M. Li, on the geometry of diffusion operators and stochastic flow, Lect. notes in Math, vol.1720, p.1720, 1999.
DOI : 10.1007/BFb0103064

K. D. Elworthy and Y. Yan, The Vanishing of harmonic one-forms on base path spaces, J. Funct. Analysis, pp.264-1168, 2013.

O. Enchev and D. Stroock, Towards a Riemannian Geometry on the Path Space over a Riemannian Manifold, Journal of Functional Analysis, vol.134, issue.2, pp.392-416, 1995.
DOI : 10.1006/jfan.1995.1151

S. Fang, Inégalité du type de Poincaré sur l'espace des chemins riemanniens, C.R. Acad. Sci. Paris, pp.318-257, 1994.

S. Fang, Stochastic Anticipative Integrals on a Riemannian Manifold, Journal of Functional Analysis, vol.131, issue.1, pp.228-253, 1995.
DOI : 10.1006/jfan.1995.1088

S. Fang and P. Malliavin, Stochastic Analysis on the Path Space of a Riemannian Manifold, Journal of Functional Analysis, vol.118, issue.1, pp.249-274, 1993.
DOI : 10.1006/jfan.1993.1145

S. Fang, F. Y. Wang, and B. Wu, Transportation-cost inequality on path spaces with uniform distance, Stochastic Process, Appl, vol.118, issue.12, pp.2181-2197, 2008.

E. P. Hsu, Quasi-Invariance of the Wiener Measure on the Path Space over a Compact Riemannian Manifold, Journal of Functional Analysis, vol.134, issue.2, pp.417-450, 1995.
DOI : 10.1006/jfan.1995.1152

E. P. Hsu, Quasi-Invariance of the Wiener Measure on Path Spaces: Noncompact Case, Journal of Functional Analysis, vol.193, issue.2, pp.278-290, 2002.
DOI : 10.1006/jfan.2001.3940

E. P. Hsu, Logarithmic Sobolev Inequalities on Path Spaces Over Riemannian Manifolds, Communications in Mathematical Physics, vol.189, issue.1, pp.9-16, 1997.
DOI : 10.1007/s002200050188

A. Naber, Characterizations of bounded Ricci curvature on smooth and nonsmooth spaces, pp.1306-651

D. Stroock, An introduction to the analysis of paths on a Riemannian manifold, Math. Survey and Monographs, vol.74, 2000.
DOI : 10.1090/surv/074