2006/03/28 by Erkan Nane · 1 citation
Computer Science · Economics, Econometrics and Finance · Mathematics · #Advanced Mathematical Modeling in Engineering #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #math.PR #msc:60J65 #msc:60K99
paper · pdf · doi:10.1051/ps:2007012
published as ESAIM: P&S, March 2007, Vol. 11, pp. 147-160
arxiv created 2006/03/28 · openalex publication_date 2007/03/01 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/31
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.