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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Moments of the lifetime of conditioned Brownian motion in cones


Authors: Burgess Davis and Biao Zhang
Journal: Proc. Amer. Math. Soc. 121 (1994), 925-929
MSC: Primary 60J65; Secondary 60J05
MathSciNet review: 1195717
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Abstract: Let $ \tau $ be the time it takes standard d-dimensional Brownian motion, started at a point inside a cone $ \Gamma $ in $ {\mathbb{R}^d}$ which has aperture angle $ \theta $, to leave the cone. Burkholder has determined the smallest p, denoted $ p(\theta ,d)$, such that $ E{\tau ^p} = \infty $. We show that if $ y \in \partial \Gamma $ then the smallest p, such that $ E({\tau ^p}\vert{B_\tau } = y) = \infty $, is $ p = 2p(\theta ,d) + (d - 2)/2$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1994-1195717-5
PII: S 0002-9939(1994)1195717-5
Keywords: Conditioned Brownian motion, h-processes
Article copyright: © Copyright 1994 American Mathematical Society