Volume 11, February 2007Special Issue: "Stochastic analysis and mathematical finance" in honor of Nicole El Karoui's 60th birthday
|Page(s)||147 - 160|
|Published online||31 March 2007|
Lifetime asymptotics of iterated Brownian motion in
Department of Mathematics, Purdue University, West Lafayette, IN 47906, USA; firstname.lastname@example.org
2 Current address: Department of Statistics and Probability, Michigan State University, A413 Wells Hall, East Lansing, MI 48824-1027, USA; email@example.com
Revised: 8 September 2006
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.
Mathematics Subject Classification: 60J65 / 60K99
Key words: Iterated Brownian motion / Brownian-time Brownian motion / exit time / bounded domain / twisted domain / unbounded convex domain.
© EDP Sciences, SMAI, 2007
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