Integration by Parts Formula and Logarithmic Sobolev Inequality on the Path Space Over Loop Groups
Fang, Shizan
Ann. Probab., Tome 27 (1999) no. 1, p. 664-683 / Harvested from Project Euclid
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The geometric stochastic analysis on the Riemannian path space developed recently gives rise to the concept of tangent processes. Roughly speaking, it is the infinitesimal version of the Girsanov theorem. Using this concept, we shall establish a formula of integration by parts on the path space over a loop group. Following the martingale method developed in Capitaine, Hsu and Ledoux, we shall prove that the logarithmic Sobolev inequality holds on the full paths. As a particular case of our result, we obtain the Driver–Lohrenz’s heat kernel logarithmic Sobolev inequalities over loop groups. The stochastic parallel transport introduced by Driver will play a crucial role.
Publié le : 1999-04-15
Classification:  Tangent processes,  stochastic parallel transport,  integration by parts,  martingale representation,  60H07,  58G32,  60H30 
@article{1022677382,
     author = {Fang, Shizan},
     title = {Integration by Parts Formula and Logarithmic Sobolev Inequality on
		 the Path Space Over Loop Groups},
     journal = {Ann. Probab.},
     volume = {27},
     number = {1},
     year = {1999},
     pages = { 664-683},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1022677382}
}

Fang, Shizan. Integration by Parts Formula and Logarithmic Sobolev Inequality on
		 the Path Space Over Loop Groups. Ann. Probab., Tome 27 (1999) no. 1, pp.  664-683. http://gdmltest.u-ga.fr/item/1022677382/