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Lifetime asymptotics of iterated Brownian motion in n

Erkan Nane (2007)

ESAIM: Probability and Statistics

Let τ D ( Z ) be the first exit time of iterated Brownian motion from a domain D n started at z D and let P z [ τ D ( Z ) > t ] be its distribution. In this paper we establish the exact asymptotics of P z [ τ D ( Z ) > t ] 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 z D lim t t - 1 / 2 exp 3 2 π 2 / 3 λ D 2 / 3 t 1 / 3 P z [ τ D ( Z ) > t ] = C ( z ) , 
where C ( z ) = ( λ D 2 7 / 2 ) / 3 π ψ ( z ) D ψ ( y ) d y 2 . Here λD is the first eigenvalue of the Dirichlet Laplacian 1 2 Δ in D, and ψ is the eigenfunction corresponding...

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