6533b829fe1ef96bd1289a6f
RESEARCH PRODUCT
Transportation-cost inequality on path spaces with uniform distance
Bo WuFeng-yu WangFeng-yu WangShizan FangShizan Fangsubject
Path (topology)Statistics and ProbabilityTransportation-cost inequalityPath spaceApplied MathematicsMathematical analysisRiemannian manifoldManifoldUniform distanceQuasi-invariant flowDistribution functionModeling and SimulationBounded functionModelling and SimulationVector fieldMathematics::Differential GeometryInvariant (mathematics)Damped gradientDistribution (differential geometry)Mathematicsdescription
Abstract Let M be a complete Riemannian manifold and μ the distribution of the diffusion process generated by 1 2 ( Δ + Z ) where Z is a C 1 -vector field. When Ric − ∇ Z is bounded below and Z has, for instance, linear growth, the transportation-cost inequality with respect to the uniform distance is established for μ on the path space over M . A simple example is given to show the optimality of the condition.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2008-12-01 | Stochastic Processes and their Applications |