Lifetime Asymptotics of Iterated Brownian Motion in R
نویسنده
چکیده
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 (
منابع مشابه
Precise asymptotics in laws of the iterated logarithm for Wiener local time
In this paper, we study the asymptotic properties of the upper and lower tail probabilities of the maximum local time L∗(t) of Wiener process (Brownian motion), and obtain some precise asymptotics in the law of the iterated logarithm and the Chungs-type laws of the iterated logarithm for the supremum of Wiener local time L(x; t); x∈R; t ∈R+. c © 2003 Elsevier B.V. All rights reserved. MSC: 60F1...
متن کاملIterated Brownian Motion in Parabola-Shaped Domains
Iterated Brownian motion Zt serves as a physical model for diffusions in a crack. If τD(Z) is the first exit time of this processes from a domain D ⊂ Rn, started at z ∈ D, then Pz [τD(Z) > t] is the distribution of the lifetime of the process in D. In this paper we determine the large time asymptotics of Pz[τPα(Z) > t] which gives exponential integrability of τPα(Z) for parabola-shaped domains ...
متن کاملIterated Brownian motion in bounded domains
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-t...
متن کاملASYMPTOTICS FOR THE EXPECTED LIFETIME OF BROWNIAN MOTION ON THIN DOMAINS IN Rn
We derive a three-term asymptotic expansion for the expected lifetime of Brownian motion and for the torsional rigidity on thin domains in R, and a two-term expansion for the maximum (and corresponding maximizer) of the expected lifetime. The approach is similar to that which we used previously to study the eigenvalues of the Dirichlet Laplacian and consists of scaling the domain in one directi...
متن کاملThe effect of various conductivity and viscosity models considering Brownian motion on nanofluids mixed convection flow and heat transfer
In this paper the effect of using various models for conductivity and viscosity considering Brownian motion of nanoparticles is investigated. This study is numerically conducted inside a cavity full of Water-Al2O3 nanofluid at the case of mixed convection heat transfer. The effect of some parameters such as the nanoparticle volume fraction, Rayleigh, Richardson and Reynolds numbers has been ex...
متن کامل