2005/05/31 by Erkan Nane
Economics, Econometrics and Finance · Mathematics · #Mathematical Dynamics and Fractals #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #math.PR #msc:60J65 #msc:60K99
paper · pdf · doi:10.1016/j.spa.2005.10.007
published as Stochastic Processes and Their Applications, 116 (2006), 905-916. · 17 pages
arxiv created 2005/10/07 · openalex publication_date 2006/01/05 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/01
Let τD(Z) is the first exit time of iterated Brownian motion from a domain D ⊂ \RRRn started at z∈ D and let Pz[τD(Z) >t] be its distribution. In this paper we establish the exact asymptotics of Pz[τD(Z) >t] over bounded domains as an extension of the result in DeBlassie \citedeblassie, for z∈ D Pz[τD(Z)>t]≈ t1/2 exp(-3/2π2/3λD2/3t1/3), as t→∞ . We also study asymptotics of the life time of Brownian-time Brownian motion (BTBM), Z1t=z+X(Y(t)), where Xt and Yt are independent one-dimensional Brownian motions.