First passage times for subordinate Brownian motions

Mateusz Kwaśnicki, Jacek Małecki and Michał Ryznar

Stochastic Processes and their Applications, 2013, vol. 123, issue 5, 1820-1850

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+.

Keywords: Lévy process; Subordinate process; First passage time; Supremum functional (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1016/j.spa.2013.01.011

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