6533b85bfe1ef96bd12bb303
RESEARCH PRODUCT
A Weitzenböck formula for the damped Ornstein–Uhlenbeck operator in adapted differential geometry
Shizan FangAna Bela Cruzeirosubject
Dirichlet formScalar (mathematics)Mathematical analysisOrnstein–Uhlenbeck processGeneral MedicineRiemannian geometrysymbols.namesakeMathematics::ProbabilityDifferential geometrysymbolsVector fieldOrnstein–Uhlenbeck operatorRicci curvatureMathematicsdescription
Abstract On the Riemannian path space we consider the Ornstein–Uhlenbeck operator associated to the Dirichlet form E (f,g)=E〈 ∇ f, ∇ g〉 H , where ∇ is the damped gradient and 〈·,·〉 H the scalar product of the Cameron–Martin space H . We prove a corresponding Weitzenbock formula restricted to adapted vector fileds: the Ricci-tensor is shown to be equal to the identity.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2001-03-01 | Comptes Rendus de l'Académie des Sciences - Series I - Mathematics |