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Iterated Brownian motion in bounded domains in

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  • Nane, Erkan

Abstract

Let [tau]D(Z) be the first exit time of iterated Brownian motion from a domain started at z[set membership, variant]D and let Pz[[tau]D(Z)>t] be its distribution. In this paper we establish the exact asymptotics of Pz[[tau]D(Z)>t] over bounded domains as an extension of the result in [R.D. DeBlassie, Iterated Brownian motion in an open set, Ann. Appl. Probab. 14 (3) (2004) 1529-1558], for z[set membership, variant]D: We also study asymptotics of the life time of Brownian-time Brownian motion (BTBM), , where Xt and Yt are independent one-dimensional Brownian motions.

Suggested Citation

  • Nane, Erkan, 2006. "Iterated Brownian motion in bounded domains in," Stochastic Processes and their Applications, Elsevier, vol. 116(6), pages 905-916, June.
    • Handle: RePEc:eee:spapps:v:116:y:2006:i:6:p:905-916
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    Cited by:

    1. Nane, Erkan, 2008. "Isoperimetric-type inequalities for iterated Brownian motion in," Statistics & Probability Letters, Elsevier, vol. 78(1), pages 90-95, January.
    2. Gajda, Janusz & Magdziarz, Marcin, 2014. "Large deviations for subordinated Brownian motion and applications," Statistics & Probability Letters, Elsevier, vol. 88(C), pages 149-156.
    3. Nane, Erkan, 2009. "Laws of the iterated logarithm for a class of iterated processes," Statistics & Probability Letters, Elsevier, vol. 79(16), pages 1744-1751, August.

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