Abstract
We give an exposition of a result of Borell (Commun Math Phys 86:143–147, 1982) that the probability function that Brownian motion hits the inner boundary before time t and before hitting the outer boundary is a space-time quasiconcave function.
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Acknowledgements
This article is written under the guidance of my adviser Professor Elton P Hsu. I would like to offer my sincerest thanks for his help and support. The author gratefully acknowledges financial support from China Scholarship Council. The author is supported by Chinese Government Scholarship (Grant No. 201606340046).
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Suo, J. A Quasiconcavity Property for the Heat Equation in a Convex Ring. Commun. Math. Stat. 8, 453–462 (2020). https://doi.org/10.1007/s40304-020-00207-6
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DOI: https://doi.org/10.1007/s40304-020-00207-6