Poincaré-type inequalities via stochastic integrals

  • Louis H. Y. Chen
Article
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Summary

Martingales and stochastic integrals are applied to prove Poincaré-type inequalities involving probability distributions on the Euclidean space. These inequalities generalize and improve several results in the literature and are shown to yield weighted Poincaré inequalities on some special compact manifolds. This leads to a new method of calculating all the eigenvalues and eigenfunctions of the Laplacian on then-sphere. As a by-product the eigenvalues are shown to be related to the moments of a probability distribution.

Keywords

Representation Formula Multivariate Normal Distribution Discontinuity Point Stochastic Integral Divisible Distribution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Copyright information

© Springer-Verlag 1985

Authors and Affiliations

  • Louis H. Y. Chen
    • 1
  1. 1.Department of MathematicsNational University of SingaporeSingaporeRepublic of Singapore

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