6533b858fe1ef96bd12b6430

RESEARCH PRODUCT

Hamilton–Jacobi semi-groups in infinite dimensional spaces

Jinghai ShaoJinghai Shao

subject

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 measure

description

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.

yearjournalcountryeditionlanguage
2006-12-01Bulletin des Sciences Mathématiques
https://doi.org/10.1016/j.bulsci.2006.03.001