Stochastic Taylor Formulas and Riemannian Geometry

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


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.


Riemannian Manifold Ricci Tensor Exit Time Standard Brownian Motion Infinitesimal Generator 
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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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