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First passage times for subordinate Brownian motions

Author

Listed:
  • Kwaśnicki, Mateusz
  • Małecki, Jacek
  • Ryznar, Michał

Abstract

Let Xt be a subordinate Brownian motion, and suppose that the Lévy measure of the underlying subordinator has a completely monotone density. Under very mild conditions, we find integral formulae for the tail distribution P(τx>t) of first passage times τx through a barrier at x>0, and its derivatives in t. As a corollary, we examine the asymptotic behaviour of P(τx>t) and its t-derivatives, either as t→∞ or x→0+.

Suggested Citation

  • Kwaśnicki, Mateusz & Małecki, Jacek & Ryznar, Michał, 2013. "First passage times for subordinate Brownian motions," Stochastic Processes and their Applications, Elsevier, vol. 123(5), pages 1820-1850.
    • Handle: RePEc:eee:spapps:v:123:y:2013:i:5:p:1820-1850
    DOI: 10.1016/j.spa.2013.01.011
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    References listed on IDEAS

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    1. L. Alili & A. E. Kyprianou, 2005. "Some remarks on first passage of Levy processes, the American put and pasting principles," Papers math/0508487, arXiv.org.
    2. Kim, Panki & Song, Renming & Vondracek, Zoran, 2009. "Boundary Harnack principle for subordinate Brownian motions," Stochastic Processes and their Applications, Elsevier, vol. 119(5), pages 1601-1631, May.
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    Cited by:

    1. Fotopoulos, Stergios & Jandhyala, Venkata & Wang, Jun, 2015. "On the joint distribution of the supremum functional and its last occurrence for subordinated linear Brownian motion," Statistics & Probability Letters, Elsevier, vol. 106(C), pages 149-156.

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