Fokker-Planck equation with respect to heat measures on loop groups

@article{Fang2011FokkerPlanckEW,
  title={Fokker-Planck equation with respect to heat measures on loop groups},
  author={Shizan Fang and Jinghai Shao},
  journal={Bulletin Des Sciences Mathematiques},
  year={2011},
  volume={135},
  pages={775-794}
}
  • S. FangJ. Shao
  • Published 1 September 2011
  • Mathematics
  • Bulletin Des Sciences Mathematiques
View via Publisher
doi.org
2 Citations

2 Citations

Perelmanʼs W-entropy for the Fokker–Planck equation over complete Riemannian manifolds

Geometry on the Wasserstein Space Over a Compact Riemannian Manifold

We revisit the intrinsic differential geometry of the Wasserstein space over a Riemannian manifold, due to a series of papers by Otto, Otto-Villani, Lott, Ambrosio-Gigli-Savaré, etc.

References

SHOWING 1-10 OF 25 REFERENCES

Integration on loop groups. II : heat equation for the Wiener measure

Integration on loop group. III : Asymptotic Peter-Weyl orthogonality

Optimal transport maps for Monge–Kantorovich problem on loop groups

Logarithmic Sobolev Inequalities for Pinned Loop Groups

Abstract LetGbe a connected compact type Lie group equipped with anAdG-invariant inner product on the Lie algebra g ofG. Given this data there is a well known left invariant “H1-Riemannian structure”…

Integration by Parts and Quasi-Invariance for Heat Kernel Measures on Loop Groups

Abstract Integration by parts formulas are established both for Wiener measure on the path space of a loop group and for the heat kernel measures on the loop group. The Wiener measure is defined to…

Convex functionals of probability measures and nonlinear diffusions on manifolds

Existence and stability for Fokker–Planck equations with log-concave reference measure

We study Markov processes associated with stochastic differential equations, whose non-linearities are gradients of convex functionals. We prove a general result of existence of such Markov processes…

Integration on loop groups. I. Quasi invariant measures

Wasserstein space over the Wiener space

The goal of this paper is to study optimal transportation problems and gradient flows of probability measures on the Wiener space, based on and extending fundamental results of Feyel–Üstünel.…

Hamilton-Jacobi semi-groups in infinite dimensional spaces