Iterated Brownian motion in bounded domains
نویسنده
چکیده
Let τD(Z) is the first exit time of iterated Brownian motion from a domain D ⊂ Rn 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 [14], for z ∈ D Pz[τD(Z) > t] ≈ t exp(− 3 2 πλ 2/3 D t ), as t → ∞. We also study asymptotics of the life time of Brownian-time Brownian motion (BTBM), Z1 t = z+X(Y (t)), where Xt and Yt are independent one-dimensional Brownian motions. Mathematics Subject Classification (2000): 60J65, 60K99.
منابع مشابه
Lifetime Asymptotics of Iterated Brownian Motion in R
Let τD(Z) be the first exit time of iterated Brownian motion from a domain D ⊂ Rn 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 improvement of the results in [12, 24], for z ∈ D lim t→∞ t exp( 3 2 πλ 2/3 D t )Pz[τD(Z) > t] = C(z), where C(z) = (λD2 7/2)/ √ 3π (
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