First passage times for subordinate Brownian motions

Abstract

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

24 pages, 1 figure

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Cited by in corpus (6)

• Spectral analysis of subordinate Brownian motions in half-line
• One-dimensional quasi-relativistic particle in the box
• Hitting times of points for symmetric Lévy processes with completely monotone jumps
• Spectral theory for one-dimensional symmetric Levy processes killed upon hitting the origin
• Rogers functions and fluctuation theory
• Asymptotic estimate of eigenvalues of pseudo-differential operators in an interval