The Annals of Probability

The First Exit Time of Planar Brownian Motion from The Interior Of a Parabola

Rodrigo Bañuelos, R.Dante DeBlassie, and Robert Smits

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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 $t \to \infty$.

Article information

Ann. Probab. Volume 29, Number 2 (2001), 882-901.

First available in Project Euclid: 21 December 2001

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60J65: Brownian motion [See also 58J65] 60J50: Boundary theory 60F10.

Exit times eigenfunction expansions Feynman-Kac functionals Bessel processes large deviation


Bañuelos, Rodrigo; DeBlassie, R.Dante; Smits, Robert. The First Exit Time of Planar Brownian Motion from The Interior Of a Parabola. Ann. Probab. 29 (2001), no. 2, 882--901. doi:10.1214/aop/1008956696.

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