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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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 $t \to \infty$.

Article information

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

Dates
First available in Project Euclid: 21 December 2001

Permanent link to this document
https://projecteuclid.org/euclid.aop/1008956696

Digital Object Identifier
doi:10.1214/aop/1008956696

Mathematical Reviews number (MathSciNet)
MR1849181

Zentralblatt MATH identifier
1013.60060

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

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

Citation

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. https://projecteuclid.org/euclid.aop/1008956696


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