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.
To David Nualart, with admiration and respect.
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Notes
- 1.
This means that sup x ∈ B | Af(x) + 1 | ≤ ε.
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Pinsky, M.A. (2013). Stochastic Taylor Formulas and Riemannian Geometry. In: Viens, F., Feng, J., Hu, Y., Nualart , E. (eds) Malliavin Calculus and Stochastic Analysis. Springer Proceedings in Mathematics & Statistics, vol 34. Springer, Boston, MA. https://doi.org/10.1007/978-1-4614-5906-4_2
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DOI: https://doi.org/10.1007/978-1-4614-5906-4_2
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