[1] Aida S. Differential calculus on path and loop spaces Ⅱ:Irreducibility of dirichlet forms on loop spaces. Bulletin des Sciences Mathématiques, 1998, 122(8):635-666
[2] Aida S. Logarithmic derivatives of heat kernels and Logarithmic Sobolev inequalities with unbounded diffusion coefficients on loop spaces. Journal of Functional Analysis, 2000, 174(2):430-477
[3] Aida S, Elworthy D. Differential calculus on path and loop spaces. I:Logarithmic Sobolev inequalities on path spaces. Comptes Rendus de l Académie des Sciences - Series I - Mathematics, 1995, 321(1):97-102
[4] Bismut J M. Large Deviations and the Malliavin Calculus. New York:Birkhäuser, 1984
[5] Capitaine M, Hsu E P, Ledoux M. Martingale representation and a simple proof of Logarithmic Sobolev inequalities on path spaces. Electronic Communications in Probability, 1997, 2:71-81
[6] Decreusefond L, Üstünel A S. Stochastic analysis of the fractional Brownian motion. Potential Analysis, 1999, 10(2):177-214
[7] Driver B K. A Cameron-Martin type quasi-invariance theorem for Brownian motion on a compact Riemannian manifold. Journal of Functional Analysis, 1992, 110(2):272-376
[8] Driver B K. A Cameron-Martin type quasi-invariance theorem for pinned Brownian motion on a compact Riemannian manifold. Transactions of the American Mathematical Society, 1994, 342(1):375-395
[9] Duncan T E, Hu Y Z, Pasik-Duncan B. Stochastic calculus for fractional Brownian motion I. Theory. SIAM Journal on Control and Optimization, 2000, 38(2):582-612
[10] Enchev O, Stroock D W. Pinned Brownian motion and its perturbations. Advances in Mathematics, 1996, 119(2):127-154
[11] Fang S Z, Malliavin P. Stochastic analysis on the path space of a Riemannian manifold:I. Markovian stochastic calculus. Journal of Functional Analysis, 1993, 118(1):249-274
[12] Gong F Z, Ma Z. The Log-Sobolev inequality on loop space over a compact Riemannian manifold. Journal of Functional Analysis, 1998, 157(2):599-623
[13] Gross L. Logarithmic Sobolev inequalities. American Journal of Mathematics, 1975, 97(4):1061-1083
[14] Gross L. Logarithmic Sobolev inequalities on loop groups. Journal of Functional Analysis, 1991, 102(2):268-313
[15] Hsu E P. Quasi-invariance of the Wiener measure on the path space over a compact Riemannian manifold. Journal of Functional Analysis, 1995, 134(2):417-450
[16] Hsu E P. Integration by parts in loop spaces. Mathematische Annalen, 1997, 309(2):331-339
[17] Hsu E P. Logarithmic Sobolev inequalities on path spaces over Riemannian manifolds. Communications in Mathematical Physics, 1997, 189(1):9-16
[18] Hsu E P. Stochastic Analysis on Manifolds. New York:American Mathematical Society, 2002
[19] Nualart D, Ouknine Y. Regularization of differential equations by fractional noise. Stochastic Processes and Their Applications, 2002, 102(1):103-116
[20] Samko S G, Kilbas A A, Marichev O I. Fractional Integrals and Derivatives:Theory and Applications. New York:Gordon Breach Science, 1993
[21] Sun X X, Guo F. On integration by parts formula and characterization of fractional Ornstein-Uhlenbeck process. Statistics and Probability Letters, 2015, 107(5):170-177 |