Abstract
We prove an upper bound for the escape rate of Brownian motion on a Cartan-Hadamard manifold in terms of the volume growth function. One of the ingredients of the proof is the Sobolev inequality on such manifolds.
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Grigor'yan, A., Hsu, E. (2009). Volume Growth and Escape Rate of Brownian Motion on a Cartan—Hadamard Manifold. In: Maz'ya, V. (eds) Sobolev Spaces in Mathematics II. International Mathematical Series, vol 9. Springer, New York, NY. https://doi.org/10.1007/978-0-387-85650-6_10
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DOI: https://doi.org/10.1007/978-0-387-85650-6_10
Publisher Name: Springer, New York, NY
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