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Stochastic Taylor Formulas and Riemannian Geometry

  • Mark A. Pinsky
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 34)

Abstract

Let (X t , P x ) be the standard Brownian motion on a complete Riemannian manifold. We investigate the asymptotic behavior of the moments of the exit time from a geodesic ball when the radius tends to zero. This is combined with a “stochastic Taylor formula” to obtain a new expansion for the mean value of a function on the boundary of a geodesic ball.

Keywords

Riemannian Manifold Ricci Tensor Exit Time Standard Brownian Motion Infinitesimal Generator 
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 Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Department of MathematicsNorthwestern UniversityEvanstonUSA

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