Search results for "Loop groups"

showing 2 items of 2 documents

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).

Discrete mathematicsPath (topology)Adjoint representationLie groupGirsanov theoremSpace (mathematics)Action (physics)Heat measuresLoop groupsLoop (topology)Loop groupLie algebraWasserstein distanceAnalysisMathematicsH-distanceJournal of Functional Analysis
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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.

Path (topology)Mathematics(all)Pure mathematicsGeneral MathematicsMathematical analysisTransportation cost inequalitiesMalliavin calculusHamilton–Jacobi equationHeat measuresLoop groupsLoop (topology)Hamilton–Jacobi semi-groupInfinite groupLoop groupPseudo-distanceMalliavin CalculusPolish spaceMathematicsProbability measureBulletin des Sciences Mathématiques
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