Abstract
Let $D$ be the interior of a parabola in $\mathbb{R}^2$ and $\tau_D$ the first exit time of Brownian motion from $D$. We show $-\log P(\tau_D) >t)$ behaves like $t^{1 /3}$ as $t \to \infty$.
Citation
Rodrigo Bañuelos. R. Dante DeBlassie. Robert Smits. "The First Exit Time of Planar Brownian Motion from The Interior Of a Parabola." Ann. Probab. 29 (2) 882 - 901, April 2001. https://doi.org/10.1214/aop/1008956696
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