0000000000755212
AUTHOR
Jinghai Shao
showing 3 related works from this author
Transportation cost inequalities on path and loop groups
2005
AbstractLet G be a connected Lie group with the Lie algebra G. The action of Cameron–Martin space H(G) on the path space Pe(G) introduced by L. Gross (Illinois J. Math. 36 (1992) 447) is free. Using this fact, we define the H-distance on Pe(G), which enables us to establish a transportation cost inequality on Pe(G). This method will be generalized to the path space over the loop group Le(G), so that we obtain a transportation cost inequality for heat measures on Le(G).
Hamilton–Jacobi semi-groups in infinite dimensional spaces
2006
AbstractLet (X,ρ) be a Polish space endowed with a probability measure μ. Assume that we can do Malliavin Calculus on (X,μ). Let d:X×X→[0,+∞] be a pseudo-distance. Consider QtF(x)=infy∈X{F(y)+d2(x,y)/2t}. We shall prove that QtF satisfies the Hamilton–Jacobi inequality under suitable conditions. This result will be applied to establish transportation cost inequalities on path groups and loop groups in the spirit of Bobkov, Gentil and Ledoux.
Fokker–Planck equation with respect to heat measures on loop groups
2011
Abstract The Dirichlet form on the loop group L e ( G ) with respect to the heat measure defines a Laplacian Δ DM on L e ( G ) . In this note, we will use Wasserstein distance variational method to solve the associated heat equation for a given data of finite entropy.