Search results for "Ornstein–Uhlenbeck operator"

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A Weitzenböck formula for the damped Ornstein–Uhlenbeck operator in adapted differential geometry

2001

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.

Dirichlet formScalar (mathematics)Mathematical analysisOrnstein–Uhlenbeck processGeneral MedicineRiemannian geometrysymbols.namesakeMathematics::ProbabilityDifferential geometrysymbolsVector fieldOrnstein–Uhlenbeck operatorRicci curvatureMathematicsComptes Rendus de l'Académie des Sciences - Series I - Mathematics
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Maximal regularity for Kolmogorov operators in L2 spaces with respect to invariant measures

2006

Abstract We prove an optimal embedding result for the domains of Kolmogorov (or degenerate hypoelliptic Ornstein–Uhlenbeck) operators in L 2 spaces with respect to invariant measures. We use an interpolation method together with optimal L 2 estimates for the space derivatives of T ( t ) f near t = 0 , where T ( t ) is the Ornstein–Uhlenbeck semigroup and f is any function in L 2 .

Discrete mathematicsPure mathematicsSemigroupApplied MathematicsGeneral MathematicsDegenerate energy levelsInvariant measureMathematics::ProbabilityDegenerate Ornstein–Uhlenbeck operatorHypoellipticityHypoelliptic operatorEmbeddingMaximal regularityInvariant (mathematics)MathematicsJournal de Mathématiques Pures et Appliquées
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