Search results for "Hamilton–Jacobi semi-group"

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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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