Lifetime asymptotics of iterated Brownian motion in $\mathbb{R}^{n}$
Open Access
- 31 March 2007
- journal article
- Published by EDP Sciences in ESAIM: Probability and Statistics
- Vol. 11, 147-160
- https://doi.org/10.1051/ps:2007012
Abstract
Let be the first exit time of iterated Brownian motion from a domain started at and let be its distribution. In this paper we establish the exact asymptotics of over bounded domains as an improvement of the results in DeBlassie (2004) [DeBlassie, Ann. Appl. Prob. 14 (2004) 1529–1558] and Nane (2006) [Nane, Stochastic Processes Appl. 116 (2006) 905–916], for where . Here λD is the first eigenvalue of the Dirichlet Laplacian in D, and ψ is the eigenfunction corresponding to λD. We also study lifetime asymptotics of Brownian-time Brownian motion, , where Xt and Yt are independent one-dimensional Brownian motions, in several unbounded domains. Using these results we obtain partial results for lifetime asymptotics of iterated Brownian motion in these unbounded domains.Keywords
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